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Analysis of a free boundary problem for tumor growth with Gibbs-Thomson relation and time delays

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 5, Pages : 20 - 20, 2017

Shihe Xu - (email), Meng Bai - (email), Fangwei Zhang - (email)

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Sensitivity analysis in set-valued optimization under strictly minimal efficiency

Evolution Equations and Control Theory  Volume 6, Issue 3, Pages : 427 - 436, 2017

Zhenhua Peng - (email), Zhongping Wan - (email), Weizhi Xiong - (email)

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A multiscale model for heterogeneous tumor spheroid in vitro

Mathematical Biosciences and Engineering  Volume 15, Issue 2, Pages : 361 - 392, 2017

Zhan Chen - (email), Yuting Zou - (email)

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Analysis of a Cahn--Hilliard system with non-zero Dirichlet conditions modeling tumor growth with chemotaxis

Discrete and Continuous Dynamical Systems  Volume 37, Issue 8, Pages : 4277 - 4308, 2017

Harald Garcke - (email), Kei Fong Lam - (email)

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Malaria incidence and anopheles mosquito density in irrigated and adjacent non-irrigated villages of Niono in Mali

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 3, Pages : 841 - 857, 2017

Moussa Doumbia - (email), Abdul-Aziz Yakubu - (email)

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6

Advection control in parabolic PDE systems for competitive populations

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 3, Pages : 1049 - 1072, 2017

Kokum R. De Silva - (email), Tuoc V. Phan - (email), Suzanne Lenhart - (email)

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7

Asymptotic analyses and error estimates for a Cahn--Hilliard type phase field system modelling tumor growth

Discrete and Continuous Dynamical Systems - Series S  Volume 10, Issue 1, Pages : 37 - 54, 2016

Pierluigi Colli - (email), Gianni Gilardi - (email), Elisabetta Rocca - (email), Jürgen Sprekels - (email)

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Optimal control and cost-effectiveness analysis of a three age-structured transmission dynamics of chikungunya virus

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 3, Pages : 687 - 715, 2016

Folashade B. Agusto - (email)

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Mathematical analysis and dynamic active subspaces for a long term model of HIV

Mathematical Biosciences and Engineering  Volume 14, Issue 3, Pages : 709 - 733, 2016

Tyson Loudon - (email), Stephen Pankavich - (email)

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Stability of non-autonomous difference equations with applications to transport and wave propagation on networks

Networks and Heterogeneous Media  Volume 11, Issue 4, Pages : 563 - 601, 2016

Yacine Chitour - (email), Guilherme Mazanti - (email), Mario Sigalotti - (email)

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Competition with high number of agents and a major one

Journal of Dynamics and Games  Volume 3, Issue 4, Pages : 319 - 334, 2016

Valeria De Mattei - (email)

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The shape derivative for an optimization problem in lithotripsy

Evolution Equations and Control Theory  Volume 5, Issue 3, Pages : 399 - 430, 2016

Barbara Kaltenbacher - (email), Gunther Peichl - (email)

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A nonlocal sample dependence SDE-PDE system modeling proton dynamics in a tumor

Discrete and Continuous Dynamical Systems - Series B  Volume 21, Issue 7, Pages : 2233 - 2254, 2016

Peter E. Kloeden - (email), Stefanie Sonner - (email), Christina Surulescu - (email)

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14

Approximate controllability of discrete semilinear systems and applications

Discrete and Continuous Dynamical Systems - Series B  Volume 21, Issue 6, Pages : 1803 - 1812, 2016

Hugo Leiva - (email), Jahnett Uzcategui - (email)

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Optimal harvesting policy for the Beverton--Holt model

Mathematical Biosciences and Engineering  Volume 13, Issue 4, Pages : 673 - 695, 2016

Martin Bohner - (email), Sabrina Streipert - (email)

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16

Free boundary problems for systems of Stokes equations

Discrete and Continuous Dynamical Systems - Series B  Volume 21, Issue 5, Pages : 1455 - 1468, 2016

Avner Friedman - (email)

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Higher-order sensitivity analysis in set-valued optimization under Henig efficiency

Journal of Industrial and Management Optimization  Volume 13, Issue 1, Pages : 313 - 327, 2016

Yihong Xu - (email), Zhenhua Peng - (email)

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Reproducing kernel functions for difference equations

Discrete and Continuous Dynamical Systems - Series S  Volume 8, Issue 6, Pages : 1055 - 1064, 2015

Ali Akgül - (email), Mustafa Inc - (email), Esra Karatas - (email)

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Mathematics of nonlinear acoustics

Evolution Equations and Control Theory  Volume 4, Issue 4, Pages : 447 - 491, 2015

Barbara Kaltenbacher - (email)

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20

A model of malignant gliomas throug symmetry reductions

DCDS Supplements  Volume 2015, Issue special, Pages : 974 - 980, 2015

María Rosa - (email), María S. Bruzón - (email), M. L. Gandarias - (email)

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21

Hybrid models of cell and tissue dynamics in tumor growth

Mathematical Biosciences and Engineering  Volume 12, Issue 6, Pages : 1141 - 1156, 2015

Yangjin Kim - (email), Hans G. Othmer - (email)

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22

Mathematical model and its fast numerical method for the tumor growth

Mathematical Biosciences and Engineering  Volume 12, Issue 6, Pages : 1173 - 1187, 2015

Hyun Geun Lee - (email), Yangjin Kim - (email), Junseok Kim - (email)

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A model of riots dynamics: Shocks, diffusion and thresholds

Networks and Heterogeneous Media  Volume 10, Issue 3, Pages : 443 - 475, 2015

Henri Berestycki - (email), Jean-Pierre Nadal - (email), Nancy Rodíguez - (email)

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Integrating release and dispatch policies in production models

Networks and Heterogeneous Media  Volume 10, Issue 3, Pages : 511 - 526, 2015

Dieter Armbruster - (email), Michael Herty - (email), Xinping Wang - (email), Lindu Zhao - (email)

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Extinction in discrete, competitive, multi-species patch models

Discrete and Continuous Dynamical Systems - Series B  Volume 20, Issue 6, Pages : 1583 - 1590, 2015

David M. Chan - (email), Matt McCombs - (email), Sarah Boegner - (email), Hye Jin Ban - (email), Suzanne L. Robertson - (email)

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An extension of a Theorem of V. Šverák to variable exponent spaces

Communications on Pure and Applied Analysis  Volume 14, Issue 5, Pages : 1987 - 2007, 2015

Carla Baroncini - (email), Julián Fernández Bonder - (email)

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Parameters identification for a model of T cell homeostasis

Mathematical Biosciences and Engineering  Volume 12, Issue 5, Pages : 917 - 936, 2015

Houssein Ayoub - (email), Bedreddine Ainseba - (email), Michel Langlais - (email), Rodolphe Thiébaut - (email)

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An age-structured model for the coupled dynamics of HIV and HSV-2

Mathematical Biosciences and Engineering  Volume 12, Issue 4, Pages : 803 - 840, 2015

Georgi Kapitanov - (email), Christina Alvey - (email), Katia Vogt-Geisse - (email), Zhilan Feng - (email)

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29

A double age-structured model of the co-infection of tuberculosis and HIV

Mathematical Biosciences and Engineering  Volume 12, Issue 1, Pages : 23 - 40, 2014

Georgi Kapitanov - (email)

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On a Cahn-Hilliard type phase field system related to tumor growth

Discrete and Continuous Dynamical Systems  Volume 35, Issue 6, Pages : 2423 - 2442, 2014

Pierluigi Colli - (email), Gianni Gilardi - (email), Danielle Hilhorst - (email)

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Reduction of cluster iteration maps

Journal of Geometric Mechanics  Volume 6, Issue 3, Pages : 297 - 318, 2014

Inês Cruz - (email), M. Esmeralda Sousa-Dias - (email)

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32

Parameter estimation of systems with delays via structural sensitivity analysis

Discrete and Continuous Dynamical Systems - Series B  Volume 19, Issue 8, Pages : 2521 - 2533, 2014

Krzysztof Fujarewicz - (email), Krzysztof Łakomiec - (email)

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33

The meaning of sensitivity functions in signaling pathways analysis

Discrete and Continuous Dynamical Systems - Series B  Volume 19, Issue 8, Pages : 2697 - 2707, 2014

Jaroslaw Smieja - (email), Malgorzata Kardynska - (email), Arkadiusz Jamroz - (email)

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34

Paralic confinement computations in coastal environment with interlocked areas

Discrete and Continuous Dynamical Systems - Series S  Volume 8, Issue 1, Pages : 45 - 54, 2014

Jean-Philippe Bernard - (email), Emmanuel Frénod - (email), Antoine Rousseau - (email)

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35

Sensor deployment for pipeline leakage detection via optimal boundary control strategies

Journal of Industrial and Management Optimization  Volume 11, Issue 1, Pages : 199 - 216, 2014

Chao Xu - (email), Yimeng Dong - (email), Zhigang Ren - (email), Huachen Jiang - (email), Xin Yu - (email)

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36

Model validation for a noninvasive arterial stenosis detection problem

Mathematical Biosciences and Engineering  Volume 11, Issue 3, Pages : 427 - 448, 2014

H. Thomas Banks - (email), Shuhua Hu - (email), Zackary R. Kenz - (email), Carola Kruse - (email), Simon Shaw - (email), John Whiteman - (email), Mark P. Brewin - (email), Stephen E. Greenwald - (email), Malcolm J. Birch - (email)

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37

Algebraic characterization of autonomy and controllability of behaviours of spatially invariant systems

Mathematical Control and Related Fields  Volume 4, Issue 1, Pages : 115 - 124, 2013

Amol Sasane - (email)

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38

Modeling confinement in Étang de Thau: Numerical simulations and multi-scale aspects

DCDS Supplements  Volume 2013, Issue special, Pages : 69 - 76, 2013

Jean-Philippe Bernard - (email), Emmanuel Frénod - (email), Antoine Rousseau - (email)

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39

Dynamically consistent discrete-time SI and SIS epidemic models

DCDS Supplements  Volume 2013, Issue special, Pages : 653 - 662, 2013

Lih-Ing W. Roeger - (email)

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40

Fluid-structure interaction with and without internal dissipation of the structure: A contrast study in stability

Evolution Equations and Control Theory  Volume 2, Issue 4, Pages : 563 - 598, 2013

George Avalos - (email), Roberto Triggiani - (email)

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41

Uniqueness and Hölder type stability of continuation for the linear thermoelasticity system with residual stress

Evolution Equations and Control Theory  Volume 2, Issue 4, Pages : 679 - 693, 2013

Nanhee Kim - (email)

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42

A dynamical two-dimensional traffic model in an anisotropic network

Networks and Heterogeneous Media  Volume 8, Issue 3, Pages : 663 - 684, 2013

Tibye Saumtally - (email), Jean-Patrick Lebacque - (email), Habib Haj-Salem - (email)

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43

An introduction to migration-selection PDE models

Discrete and Continuous Dynamical Systems  Volume 33, Issue 10, Pages : 4349 - 4373, 2013

Yuan Lou - (email), Thomas Nagylaki - (email), Wei-Ming Ni - (email)

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44

Generalizations of analogs of theorems of Maizel and Pliss and their application in shadowing theory

Discrete and Continuous Dynamical Systems  Volume 33, Issue 9, Pages : 4187 - 4205, 2013

Dmitry Todorov - (email)

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45

Rational decay rates for a PDE heat--structure interaction: A frequency domain approach

Evolution Equations and Control Theory  Volume 2, Issue 2, Pages : 233 - 253, 2013

George Avalos - (email), Roberto Triggiani - (email)

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46

A multiple time-scale computational model of a tumor and its micro environment

Mathematical Biosciences and Engineering  Volume 10, Issue 1, Pages : 121 - 150, 2012

Christopher DuBois - (email), Jesse Farnham - (email), Eric Aaron - (email), Ami Radunskaya - (email)

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47

PDE problems arising in mathematical biology

Networks and Heterogeneous Media  Volume 7, Issue 4, Pages : 691 - 703, 2012

Avner Friedman - (email)

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48

Periodic solutions of second order Lagrangian difference systems with bounded or singular $\phi$-Laplacian and periodic potential

Discrete and Continuous Dynamical Systems - Series S  Volume 6, Issue 4, Pages : 1065 - 1076, 2012

Jean Mawhin - (email)

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49

A division-dependent compartmental model for computing cell numbers in CFSE-based lymphocyte proliferation assays

Mathematical Biosciences and Engineering  Volume 9, Issue 4, Pages : 699 - 736, 2012

H. Thomas Banks - (email), W. Clayton Thompson - (email), Cristina Peligero - (email), Sandra Giest - (email), Jordi Argilaguet - (email), Andreas Meyerhans - (email)

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50

Lyapunov inequalities for partial differential equations at radial higher eigenvalues

Discrete and Continuous Dynamical Systems  Volume 33, Issue 1, Pages : 111 - 122, 2012

Antonio Cañada - (email), Salvador Villegas - (email)

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51

Local well-posedness of quasi-linear systems generalizing KdV

Communications on Pure and Applied Analysis  Volume 12, Issue 2, Pages : 899 - 921, 2012

Timur Akhunov - (email)

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52

Parameter estimation and uncertainty quantification for an epidemic model

Mathematical Biosciences and Engineering  Volume 9, Issue 3, Pages : 553 - 576, 2012

Alex Capaldi - (email), Samuel Behrend - (email), Benjamin Berman - (email), Jason Smith - (email), Justin Wright - (email), Alun L. Lloyd - (email)

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53

Modeling the effects of introducing a new antibiotic in a hospital setting: A case study

Mathematical Biosciences and Engineering  Volume 9, Issue 3, Pages : 601 - 625, 2012

Michele L. Joyner - (email), Cammey C. Manning - (email), Brandi N. Canter - (email)

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54

Conservation laws in mathematical biology

Discrete and Continuous Dynamical Systems  Volume 32, Issue 9, Pages : 3081 - 3097, 2012

Avner Friedman - (email)

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55

Adaptation of an ecological territorial model to street gang spatial patterns in Los Angeles

Discrete and Continuous Dynamical Systems  Volume 32, Issue 9, Pages : 3223 - 3244, 2012

Laura M. Smith - (email), Andrea L. Bertozzi - (email), P. Jeffrey Brantingham - (email), George E. Tita - (email), Matthew Valasik - (email)

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56

Compactness of discrete approximate solutions to parabolic PDEs - Application to a turbulence model

Communications on Pure and Applied Analysis  Volume 11, Issue 6, Pages : 2371 - 2391, 2012

T. Gallouët - (email), J.-C. Latché - (email)

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57

Carleman estimates for some anisotropic elasticity systems and applications

Evolution Equations and Control Theory  Volume 1, Issue 1, Pages : 141 - 154, 2012

Victor Isakov - (email)

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Macrotransport in nonlinear, reactive, shear flows

Communications on Pure and Applied Analysis  Volume 11, Issue 5, Pages : 2125 - 2146, 2012

Eric S. Wright - (email)

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59

Stable manifolds with optimal regularity for difference equations

Discrete and Continuous Dynamical Systems  Volume 32, Issue 5, Pages : 1537 - 1555, 2012

Luis Barreira - (email), Claudia Valls - (email)

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60

Controlling malaria with indoor residual spraying in spatially heterogenous environments

Mathematical Biosciences and Engineering  Volume 8, Issue 4, Pages : 889 - 914, 2011

Mo'tassem Al-Arydah - (email), Robert Smith? - (email)

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Morphogenesis and aggressiveness of cervix carcinoma

Mathematical Biosciences and Engineering  Volume 8, Issue 4, Pages : 987 - 997, 2011

Elena Izquierdo-Kulich - (email), Margarita Amigó de Quesada - (email), Carlos Manuel Pérez-Amor - (email), José Manuel Nieto-Villar - (email)

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Tumor cells proliferation and migration under the influence of their microenvironment

Mathematical Biosciences and Engineering  Volume 8, Issue 2, Pages : 371 - 383, 2011

Avner Friedman - (email), Yangjin Kim - (email)

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63

Well-posedness and stability analysis for a moving boundary problem modelling the growth of nonnecrotic tumors

Discrete and Continuous Dynamical Systems - Series B  Volume 15, Issue 3, Pages : 573 - 596, 2011

Joachim Escher - (email), Anca-Voichita Matioc - (email)

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Nirenberg's contributions to complex analysis

Discrete and Continuous Dynamical Systems  Volume 30, Issue 2, Pages : 537 - 545, 2011

Joseph J Kohn - (email)

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65

An effective design method to produce stationary chemical reaction-diffusion patterns

Communications on Pure and Applied Analysis  Volume 11, Issue 1, Pages : 189 - 207, 2010

Patrick De Kepper - (email), István Szalai - (email)

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A method for analyzing the stability of the resting state for a model of pacemaker cells surrounded by stable cells

Mathematical Biosciences and Engineering  Volume 7, Issue 3, Pages : 505 - 526, 2010

Robert Artebrant - (email), Aslak Tveito - (email), Glenn T. Lines - (email)

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Discrete and continuous random water wave dynamics

Discrete and Continuous Dynamical Systems  Volume 28, Issue 4, Pages : 1603 - 1633, 2010

André Nachbin - (email)

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68

On the regularity of minimizers to degenerate functionals

Communications on Pure and Applied Analysis  Volume 9, Issue 5, Pages : 1311 - 1318, 2010

P. Di Gironimo - (email), L. D’Onofrio - (email)

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Level set based brain aneurysm capturing in 3D

Inverse Problems and Imaging  Volume 4, Issue 2, Pages : 241 - 255, 2010

Bin Dong - (email), Aichi Chien - (email), Yu Mao - (email), Jian Ye - (email), Fernando Vinuela - (email), Stanley Osher - (email)

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Asymptotic behavior of solutions for parabolic differential equations with invariance and applications to a free boundary problem modeling tumor growth

Discrete and Continuous Dynamical Systems  Volume 26, Issue 2, Pages : 737 - 765, 2009

Junde Wu - (email), Shangbin Cui - (email)

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71

The dynamics of tumor growth and cells pattern morphology

Mathematical Biosciences and Engineering  Volume 6, Issue 3, Pages : 547 - 559, 2009

Elena Izquierdo-Kulich - (email), Margarita Amigó de Quesada - (email), Carlos Manuel Pérez-Amor - (email), Magda Lopes Texeira - (email), José Manuel Nieto-Villar - (email)

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72

Asymptotic behavior of solutions of a free boundary problem modelling the growth of tumors with Stokes equations

Discrete and Continuous Dynamical Systems  Volume 24, Issue 2, Pages : 625 - 651, 2009

Junde Wu - (email), Shangbin Cui - (email)

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The role of feedback in the formation of morphogen territories

Mathematical Biosciences and Engineering  Volume 5, Issue 2, Pages : 277 - 298, 2008

David Iron - (email), Adeela Syed - (email), Heidi Theisen - (email), Tamas Lukacsovich - (email), Mehrangiz Naghibi - (email), Lawrence J. Marsh - (email), Frederic Y. M. Wan - (email), Qing Nie - (email)

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Morphogenesis of the tumor patterns

Mathematical Biosciences and Engineering  Volume 5, Issue 2, Pages : 299 - 313, 2008

Elena Izquierdo-Kulich - (email), José Manuel Nieto-Villar - (email)

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Mathematical analysis of a PDE epidemiological model applied to scrapie transmission

Communications on Pure and Applied Analysis  Volume 7, Issue 3, Pages : 659 - 675, 2008

Najat Ziyadi - (email), Said Boulite - (email), M. Lhassan Hbid - (email), Suzanne Touzeau - (email)

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76

An existence result for a P.D.E. with hysteresis, convection and a nonlinear boundary condition

DCDS Supplements  Volume 2007, Issue Special, Pages : 344 - 353, 2007

Michela Eleuteri - (email)

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An asymptotic convergence result for a system of partial differential equations with hysteresis

Communications on Pure and Applied Analysis  Volume 6, Issue 4, Pages : 1131 - 1143, 2007

Michela Eleuteri - (email), Pavel Krejčí - (email)

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Mesoscopic model for tumor growth

Mathematical Biosciences and Engineering  Volume 4, Issue 4, Pages : 687 - 698, 2007

Elena Izquierdo-Kulich - (email), José Manuel Nieto-Villar - (email)

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Renormalization group analysis of nonlinear diffusion equations with time dependent coefficients: Analytical results

Discrete and Continuous Dynamical Systems - Series B  Volume 7, Issue 4, Pages : 699 - 715, 2007

G. A. Braga - (email), Frederico Furtado - (email), Jussara M. Moreira - (email), Leonardo T. Rolla - (email)

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Brain anatomical feature detection by solving partial differential equations on general manifolds

Discrete and Continuous Dynamical Systems - Series B  Volume 7, Issue 3, Pages : 605 - 618, 2007

Lok Ming Lui - (email), Yalin Wang - (email), Tony F. Chan - (email), Paul M. Thompson - (email)

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Visualisation of the numerical solution of partial differential equation systems in three space dimensions and its importance for mathematical models in biology

Mathematical Biosciences and Engineering  Volume 3, Issue 4, Pages : 571 - 582, 2006

Heiko Enderling - (email), Alexander R.A. Anderson - (email), Mark A.J. Chaplain - (email), Glenn W.A. Rowe - (email)

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Generalized support set invariancy sensitivity analysis in linear optimization

Journal of Industrial and Management Optimization  Volume 2, Issue 1, Pages : 1 - 18, 2006

Alireza Ghaffari Hadigheh - (email), Tamás Terlaky - (email)

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Controllability of couette flows

Communications on Pure and Applied Analysis  Volume 5, Issue 1, Pages : 201 - 211, 2005

Michael Schmidt - (email), Emmanuel Trélat - (email)

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Renormalization group calculation of asymptotically self-similar dynamics

DCDS Supplements  Volume 2005, Issue Special, Pages : 131 - 141, 2005

G. A. Braga - (email), Frederico Furtado - (email), Vincenzo Isaia - (email)

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85

Interstitial Pressure And Fluid Motion In Tumor Cords

Mathematical Biosciences and Engineering  Volume 2, Issue 3, Pages : 445 - 460, 2005

Alessandro Bertuzzi - (email), Antonio Fasano - (email), Alberto Gandolfi - (email), Carmela Sinisgalli - (email)

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86

Modeling Multicellular Systems Using Subcellular Elements

Mathematical Biosciences and Engineering  Volume 2, Issue 3, Pages : 613 - 624, 2005

T. J. Newman - (email)

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A General Mathematical Method for Investigating the Thymic Microenvironment, Thymocyte Development, and Immunopathogenesis

Mathematical Biosciences and Engineering  Volume 1, Issue 2, Pages : 289 - 305, 2004

Guanyu Wang - (email), Gerhard R. F. Krueger - (email)

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Periodic solutions of a class of nonautonomous discrete time semi-ratio-dependent predator-prey systems

Discrete and Continuous Dynamical Systems - Series B  Volume 4, Issue 3, Pages : 563 - 574, 2004

Meng Fan - (email), Qian Wang - (email)

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Dynamics of vertical delay endomorphisms

Discrete and Continuous Dynamical Systems - Series B  Volume 3, Issue 3, Pages : 409 - 422, 2003

N. Romero - (email), A. Rovella - (email), F. Vilamajó - (email)

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Analysis and numerical approximation of a class of two-way diffusions

Communications on Pure and Applied Analysis  Volume 2, Issue 1, Pages : 91 - 99, 2002

G. Wei - (email), P. Clifford - (email)

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Global existence of solutions to a reaction diffusion system based upon carbonate reaction kinetics

Communications on Pure and Applied Analysis  Volume 1, Issue 1, Pages : 77 - 84, 2001

Congming Li - (email), Eric S. Wright - (email)

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On Maxwell's system with a thermal effect

Discrete and Continuous Dynamical Systems - Series B  Volume 1, Issue 4, Pages : 485 - 494, 2001

J. J. Morgan - (email), Hong-Ming Yin - (email)

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