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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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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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A family of self-avoiding random walks interpolating the loop-erased random walk and a self-avoiding walk on the Sierpiński gasket

Discrete and Continuous Dynamical Systems - Series S  Volume 10, Issue 2, Pages : 289 - 311, 2017

Kumiko Hattori - (email), Noriaki Ogo - (email), Takafumi Otsuka - (email)

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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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Adjoint sensitivity analysis of a tumor growth model and its application to spatiotemporal radiotherapy optimization

Mathematical Biosciences and Engineering  Volume 13, Issue 6, Pages : 1131 - 1142, 2016

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

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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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Theoretical properties of fractal dimensions for fractal structures

Discrete and Continuous Dynamical Systems - Series S  Volume 8, Issue 6, Pages : 1113 - 1128, 2015

Manuel Fernández-Martínez - (email)

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Generating pre-fractals to approach real IFS-attractors with a fixed Hausdorff dimension

Discrete and Continuous Dynamical Systems - Series S  Volume 8, Issue 6, Pages : 1129 - 1137, 2015

Manuel Fernández-Martínez - (email), Miguel Ángel López Guerrero - (email)

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A stochastic model for microbial fermentation process under Gaussian white noise environment

Numerical Algebra, Control and Optimization  Volume 5, Issue 4, Pages : 381 - 392, 2015

Yan Wang - (email), Lei Wang - (email), Yanxiang Zhao - (email), Aimin Song - (email), Yanping Ma - (email)

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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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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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An aggregate stochastic model incorporating individual dynamics for predation movements of anelosimus studiosus

Mathematical Biosciences and Engineering  Volume 12, Issue 3, Pages : 585 - 607, 2015

Alex John Quijano - (email), Michele L. Joyner - (email), Edith Seier - (email), Nathaniel Hancock - (email), Michael Largent - (email), Thomas C. Jones - (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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Modeling DNA thermal denaturation at the mesoscopic level

Discrete and Continuous Dynamical Systems - Series B  Volume 19, Issue 8, Pages : 2469 - 2482, 2014

Marina Dolfin - (email), Mirosław Lachowicz - (email)

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Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology

Mathematical Biosciences and Engineering  Volume 11, Issue 3, Pages : 403 - 425, 2014

Edward J. Allen - (email)

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A non-autonomous stochastic predator-prey model

Mathematical Biosciences and Engineering  Volume 11, Issue 2, Pages : 167 - 188, 2013

Aniello Buonocore - (email), Luigia Caputo - (email), Enrica Pirozzi - (email), Amelia G. Nobile - (email)

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Numerical simulation of nonlinear dispersive quantization

Discrete and Continuous Dynamical Systems  Volume 34, Issue 3, Pages : 991 - 1008, 2013

Gong Chen - (email), Peter J. Olver - (email)

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Sequences of compatible periodic hybrid orbits of prefractal Koch snowflake billiards

Discrete and Continuous Dynamical Systems  Volume 33, Issue 8, Pages : 3719 - 3740, 2013

Michel L. Lapidus - (email), Robert G. Niemeyer - (email)

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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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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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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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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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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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Eventual regularization of the slightly supercritical fractional Burgers equation

Discrete and Continuous Dynamical Systems  Volume 27, Issue 2, Pages : 847 - 861, 2010

Chi Hin Chan - (email), Magdalena Czubak - (email), Luis Silvestre - (email)

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Laplacians on the basilica Julia set

Communications on Pure and Applied Analysis  Volume 9, Issue 1, Pages : 211 - 231, 2009

Luke G. Rogers - (email), Alexander Teplyaev - (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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Mathematical modelling of internal HIV dynamics

Discrete and Continuous Dynamical Systems - Series B  Volume 12, Issue 2, Pages : 305 - 321, 2009

Nirav Dalal - (email), David Greenhalgh - (email), Xuerong Mao - (email)

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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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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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32

Hausdorff dimension of self-affine limit sets with an invariant direction

Discrete and Continuous Dynamical Systems  Volume 21, Issue 4, Pages : 1015 - 1023, 2008

Krzysztof Barański - (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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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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35

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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Orthogonal harmonic analysis of fractal measures

Electronic Research Announcements of the AMS  Volume 4, Issue 0, Pages : 35 - 42,

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