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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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Optimisation modelling of cancer growth

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 1, Pages : 115 - 123, 2016

Tiffany A. Jones - (email), Lou Caccetta - (email), Volker Rehbock - (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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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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Synergistic effect of blocking cancer cell invasion revealed by computer simulations

Mathematical Biosciences and Engineering  Volume 12, Issue 6, Pages : 1189 - 1202, 2015

Kazuhisa Ichikawa - (email)

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The role of the cytokines IL-27 and IL-35 in cancer

Mathematical Biosciences and Engineering  Volume 12, Issue 6, Pages : 1203 - 1217, 2015

Avner Friedman - (email), Kang-Ling Liao - (email)

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Models, measurement and inference in epithelial tissue dynamics

Mathematical Biosciences and Engineering  Volume 12, Issue 6, Pages : 1321 - 1340, 2015

Oliver J. Maclaren - (email), Helen M. Byrne - (email), Alexander G. Fletcher - (email), Philip K. Maini - (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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Regulation of Th1/Th2 cells in asthma development: A mathematical model

Mathematical Biosciences and Engineering  Volume 10, Issue 4, Pages : 1095 - 1133, 2013

Yangjin Kim - (email), Seongwon Lee - (email), You-Sun Kim - (email), Sean Lawler - (email), Yong Song Gho - (email), Yoon-Keun Kim - (email), Hyung Ju Hwang - (email)

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Computational modeling approaches to studying the dynamics of oncolytic viruses

Mathematical Biosciences and Engineering  Volume 10, Issue 3, Pages : 939 - 957, 2013

Dominik Wodarz - (email)

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A mathematical model for the immunotherapeutic control of the Th1/Th2 imbalance in melanoma

Discrete and Continuous Dynamical Systems - Series B  Volume 18, Issue 4, Pages : 1017 - 1030, 2013

Yuri Kogan - (email), Zvia Agur - (email), Moran Elishmereni - (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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Evolution of uncontrolled proliferation and the angiogenic switch in cancer

Mathematical Biosciences and Engineering  Volume 9, Issue 4, Pages : 843 - 876, 2012

John D. Nagy - (email), Dieter Armbruster - (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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Questions from the fourth son: A clinician reflects on immunomonitoring, surrogate markers and systems biology

Mathematical Biosciences and Engineering  Volume 8, Issue 2, Pages : 279 - 287, 2011

Charles Wiseman, M.D. - (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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A delay-differential equation model of HIV related cancer--immune system dynamics

Mathematical Biosciences and Engineering  Volume 8, Issue 2, Pages : 627 - 641, 2011

Urszula Foryś - (email), Jan Poleszczuk - (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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An elementary approach to modeling drug resistance in cancer

Mathematical Biosciences and Engineering  Volume 7, Issue 4, Pages : 905 - 918, 2010

Cristian Tomasetti - (email), Doron Levy - (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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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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On the global dynamics of a model for tumor immunotherapy

Mathematical Biosciences and Engineering  Volume 6, Issue 3, Pages : 573 - 583, 2009

Denise E. Kirschner - (email), Alexei Tsygvintsev - (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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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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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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Modeling Cancer in HIV-1 Infected Individuals: Equilibria, Cycles and Chaotic Behavior

Mathematical Biosciences and Engineering  Volume 3, Issue 2, Pages : 313 - 324, 2006

Jie Lou - (email), Tommaso Ruggeri - (email), Claudio Tebaldi - (email)

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Using Mathematical Modeling as a Resource in Clinical Trials

Mathematical Biosciences and Engineering  Volume 2, Issue 3, Pages : 421 - 436, 2005

Evans K. Afenya - (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

Immunotherapy: An Optimal Control Theory Approach

Mathematical Biosciences and Engineering  Volume 2, Issue 3, Pages : 499 - 510, 2005

K. Renee Fister - (email), Jennifer Hughes Donnelly - (email)

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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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The Ecology and Evolutionary Biology of Cancer: A Review of Mathematical Models of Necrosis and Tumor Cell Diversity

Mathematical Biosciences and Engineering  Volume 2, Issue 2, Pages : 381 - 418, 2005

John D. Nagy - (email)

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Optimal control applied to immunotherapy

Discrete and Continuous Dynamical Systems - Series B  Volume 4, Issue 1, Pages : 135 - 146, 2003

Thalya Burden - (email), Jon Ernstberger - (email), K. Renee Fister - (email)

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A hierarchy of cancer models and their mathematical challenges

Discrete and Continuous Dynamical Systems - Series B  Volume 4, Issue 1, Pages : 147 - 159, 2003

Avner Friedman - (email)

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