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Fast reaction limit and long time behavior for a competition-diffusion system with Dirichlet boundary conditions
An age and spatially structured model of tumor invasion with haptotaxis
1. | Department of Mathematics, Mansfield College, Oxford University, Oxford, England |
2. | Depto. de Matemática Aplicada, E.T.S.I. Industriales, c. José Gutiérrez Abascal, 2, 28006 Madrid |
3. | Dipartimento di Matematica Pura e Applicata, Universita' di Padova, Padua |
4. | Mathematics Department, Vanderbilt University, Nashville, TN 37240, United States |
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Chunhua Jin. Boundedness and global solvability to a chemotaxis-haptotaxis model with slow and fast diffusion. Discrete and Continuous Dynamical Systems - B, 2018, 23 (4) : 1675-1688. doi: 10.3934/dcdsb.2018069 |
[2] |
Jiashan Zheng. Boundedness of solutions to a quasilinear higher-dimensional chemotaxis-haptotaxis model with nonlinear diffusion. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 627-643. doi: 10.3934/dcds.2017026 |
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Sebastián Ferrer, Francisco Crespo. Parametric quartic Hamiltonian model. A unified treatment of classic integrable systems. Journal of Geometric Mechanics, 2014, 6 (4) : 479-502. doi: 10.3934/jgm.2014.6.479 |
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Ghendrih Philippe, Hauray Maxime, Anne Nouri. Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solution. Kinetic and Related Models, 2009, 2 (4) : 707-725. doi: 10.3934/krm.2009.2.707 |
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Elisabeth Logak, Chao Wang. The singular limit of a haptotaxis model with bistable growth. Communications on Pure and Applied Analysis, 2012, 11 (1) : 209-228. doi: 10.3934/cpaa.2012.11.209 |
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Angela A. Albanese, Xavier Barrachina, Elisabetta M. Mangino, Alfredo Peris. Distributional chaos for strongly continuous semigroups of operators. Communications on Pure and Applied Analysis, 2013, 12 (5) : 2069-2082. doi: 10.3934/cpaa.2013.12.2069 |
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V. Pata, Sergey Zelik. A result on the existence of global attractors for semigroups of closed operators. Communications on Pure and Applied Analysis, 2007, 6 (2) : 481-486. doi: 10.3934/cpaa.2007.6.481 |
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Niklas Kolbe, Nikolaos Sfakianakis, Christian Stinner, Christina Surulescu, Jonas Lenz. Modeling multiple taxis: Tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence. Discrete and Continuous Dynamical Systems - B, 2021, 26 (1) : 443-481. doi: 10.3934/dcdsb.2020284 |
[9] |
Pan Zheng, Chunlai Mu, Xiaojun Song. On the boundedness and decay of solutions for a chemotaxis-haptotaxis system with nonlinear diffusion. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 1737-1757. doi: 10.3934/dcds.2016.36.1737 |
[10] |
Faker Ben Belgacem. Uniqueness for an ill-posed reaction-dispersion model. Application to organic pollution in stream-waters. Inverse Problems and Imaging, 2012, 6 (2) : 163-181. doi: 10.3934/ipi.2012.6.163 |
[11] |
Amy H. Lin. A model of tumor and lymphocyte interactions. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 241-266. doi: 10.3934/dcdsb.2004.4.241 |
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Elena Izquierdo-Kulich, José Manuel Nieto-Villar. Mesoscopic model for tumor growth. Mathematical Biosciences & Engineering, 2007, 4 (4) : 687-698. doi: 10.3934/mbe.2007.4.687 |
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Francesco Altomare, Mirella Cappelletti Montano, Vita Leonessa. On the positive semigroups generated by Fleming-Viot type differential operators. Communications on Pure and Applied Analysis, 2019, 18 (1) : 323-340. doi: 10.3934/cpaa.2019017 |
[14] |
Bertrand Lods, Mustapha Mokhtar-Kharroubi, Mohammed Sbihi. Spectral properties of general advection operators and weighted translation semigroups. Communications on Pure and Applied Analysis, 2009, 8 (5) : 1469-1492. doi: 10.3934/cpaa.2009.8.1469 |
[15] |
Jorge J. Betancor, Alejandro J. Castro, Marta De León-Contreras. Variation operators for semigroups associated with Fourier-Bessel expansions. Communications on Pure and Applied Analysis, 2022, 21 (1) : 239-273. doi: 10.3934/cpaa.2021176 |
[16] |
Didier Bresch, Thierry Colin, Emmanuel Grenier, Benjamin Ribba, Olivier Saut. A viscoelastic model for avascular tumor growth. Conference Publications, 2009, 2009 (Special) : 101-108. doi: 10.3934/proc.2009.2009.101 |
[17] |
Denise E. Kirschner, Alexei Tsygvintsev. On the global dynamics of a model for tumor immunotherapy. Mathematical Biosciences & Engineering, 2009, 6 (3) : 573-583. doi: 10.3934/mbe.2009.6.573 |
[18] |
Kentarou Fujie, Akio Ito, Michael Winkler, Tomomi Yokota. Stabilization in a chemotaxis model for tumor invasion. Discrete and Continuous Dynamical Systems, 2016, 36 (1) : 151-169. doi: 10.3934/dcds.2016.36.151 |
[19] |
Daniel Vasiliu, Jianjun Paul Tian. Periodic solutions of a model for tumor virotherapy. Discrete and Continuous Dynamical Systems - S, 2011, 4 (6) : 1587-1597. doi: 10.3934/dcdss.2011.4.1587 |
[20] |
Rudolf Olach, Vincent Lučanský, Božena Dorociaková. The model of nutrients influence on the tumor growth. Discrete and Continuous Dynamical Systems - B, 2022, 27 (5) : 2607-2619. doi: 10.3934/dcdsb.2021150 |
2021 Impact Factor: 1.497
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