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Existence and asymptotic behavior of solutions to a moving boundary problem modeling the growth of multi-layer tumors
1. | Department of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640 |
2. | Department of Mathematics, Sun Yat-Sen University, Guangzhou, Guangdong 510275, China |
[1] |
Junde Wu, Shangbin Cui. Asymptotic behavior of solutions of a free boundary problem modelling the growth of tumors with Stokes equations. Discrete and Continuous Dynamical Systems, 2009, 24 (2) : 625-651. doi: 10.3934/dcds.2009.24.625 |
[2] |
Joachim Escher, Anca-Voichita Matioc. Well-posedness and stability analysis for a moving boundary problem modelling the growth of nonnecrotic tumors. Discrete and Continuous Dynamical Systems - B, 2011, 15 (3) : 573-596. doi: 10.3934/dcdsb.2011.15.573 |
[3] |
T. Tachim Medjo. Multi-layer quasi-geostrophic equations of the ocean with delays. Discrete and Continuous Dynamical Systems - B, 2008, 10 (1) : 171-196. doi: 10.3934/dcdsb.2008.10.171 |
[4] |
Haigang Li, Jenn-Nan Wang, Ling Wang. Refined stability estimates in electrical impedance tomography with multi-layer structure. Inverse Problems and Imaging, 2022, 16 (1) : 229-249. doi: 10.3934/ipi.2021048 |
[5] |
Jinsen Zhuang, Yan Zhou, Yonghui Xia. Synchronization analysis of drive-response multi-layer dynamical networks with additive couplings and stochastic perturbations. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1607-1629. doi: 10.3934/dcdss.2020279 |
[6] |
Djano Kandaswamy, Thierry Blu, Dimitri Van De Ville. Analytic sensing for multi-layer spherical models with application to EEG source imaging. Inverse Problems and Imaging, 2013, 7 (4) : 1251-1270. doi: 10.3934/ipi.2013.7.1251 |
[7] |
François Bouchut, Vladimir Zeitlin. A robust well-balanced scheme for multi-layer shallow water equations. Discrete and Continuous Dynamical Systems - B, 2010, 13 (4) : 739-758. doi: 10.3934/dcdsb.2010.13.739 |
[8] |
T. Tachim Medjo. Averaging of a multi-layer quasi-geostrophic equations with oscillating external forces. Communications on Pure and Applied Analysis, 2014, 13 (3) : 1119-1140. doi: 10.3934/cpaa.2014.13.1119 |
[9] |
Qingshan Chen. On the well-posedness of the inviscid multi-layer quasi-geostrophic equations. Discrete and Continuous Dynamical Systems, 2019, 39 (6) : 3215-3237. doi: 10.3934/dcds.2019133 |
[10] |
Hua Chen, Shaohua Wu. The moving boundary problem in a chemotaxis model. Communications on Pure and Applied Analysis, 2012, 11 (2) : 735-746. doi: 10.3934/cpaa.2012.11.735 |
[11] |
X. Liang, Roderick S. C. Wong. On a Nested Boundary-Layer Problem. Communications on Pure and Applied Analysis, 2009, 8 (1) : 419-433. doi: 10.3934/cpaa.2009.8.419 |
[12] |
Jie Wang, Xiaoqiang Wang. New asymptotic analysis method for phase field models in moving boundary problem with surface tension. Discrete and Continuous Dynamical Systems - B, 2015, 20 (9) : 3185-3213. doi: 10.3934/dcdsb.2015.20.3185 |
[13] |
Junde Wu. Bifurcation for a free boundary problem modeling the growth of necrotic multilayered tumors. Discrete and Continuous Dynamical Systems, 2019, 39 (6) : 3399-3411. doi: 10.3934/dcds.2019140 |
[14] |
Liping Wang, Chunyi Zhao. Solutions with clustered bubbles and a boundary layer of an elliptic problem. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 2333-2357. doi: 10.3934/dcds.2014.34.2333 |
[15] |
Liping Wang, Juncheng Wei. Solutions with interior bubble and boundary layer for an elliptic problem. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 333-351. doi: 10.3934/dcds.2008.21.333 |
[16] |
O. Guès, G. Métivier, M. Williams, K. Zumbrun. Boundary layer and long time stability for multi-D viscous shocks. Discrete and Continuous Dynamical Systems, 2004, 11 (1) : 131-160. doi: 10.3934/dcds.2004.11.131 |
[17] |
Christos Sourdis. Analysis of an irregular boundary layer behavior for the steady state flow of a Boussinesq fluid. Discrete and Continuous Dynamical Systems, 2017, 37 (2) : 1039-1059. doi: 10.3934/dcds.2017043 |
[18] |
Masahiro Suzuki. Asymptotic stability of a boundary layer to the Euler--Poisson equations for a multicomponent plasma. Kinetic and Related Models, 2016, 9 (3) : 587-603. doi: 10.3934/krm.2016008 |
[19] |
Huijuan Song, Bei Hu, Zejia Wang. Stationary solutions of a free boundary problem modeling the growth of vascular tumors with a necrotic core. Discrete and Continuous Dynamical Systems - B, 2021, 26 (1) : 667-691. doi: 10.3934/dcdsb.2020084 |
[20] |
Junde Wu, Shangbin Cui. 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, 2010, 26 (2) : 737-765. doi: 10.3934/dcds.2010.26.737 |
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