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Existence and asymptotic behavior of solutions to a moving boundary problem modeling the growth of multilayer tumors
1.  Department of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640 
2.  Department of Mathematics, Sun YatSen 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 & Continuous Dynamical Systems  A, 2009, 24 (2) : 625651. doi: 10.3934/dcds.2009.24.625 
[2] 
Joachim Escher, AncaVoichita Matioc. Wellposedness and stability analysis for a moving boundary problem modelling the growth of nonnecrotic tumors. Discrete & Continuous Dynamical Systems  B, 2011, 15 (3) : 573596. doi: 10.3934/dcdsb.2011.15.573 
[3] 
T. Tachim Medjo. Multilayer quasigeostrophic equations of the ocean with delays. Discrete & Continuous Dynamical Systems  B, 2008, 10 (1) : 171196. doi: 10.3934/dcdsb.2008.10.171 
[4] 
Djano Kandaswamy, Thierry Blu, Dimitri Van De Ville. Analytic sensing for multilayer spherical models with application to EEG source imaging. Inverse Problems & Imaging, 2013, 7 (4) : 12511270. doi: 10.3934/ipi.2013.7.1251 
[5] 
François Bouchut, Vladimir Zeitlin. A robust wellbalanced scheme for multilayer shallow water equations. Discrete & Continuous Dynamical Systems  B, 2010, 13 (4) : 739758. doi: 10.3934/dcdsb.2010.13.739 
[6] 
T. Tachim Medjo. Averaging of a multilayer quasigeostrophic equations with oscillating external forces. Communications on Pure & Applied Analysis, 2014, 13 (3) : 11191140. doi: 10.3934/cpaa.2014.13.1119 
[7] 
Qingshan Chen. On the wellposedness of the inviscid multilayer quasigeostrophic equations. Discrete & Continuous Dynamical Systems  A, 2019, 39 (6) : 32153237. doi: 10.3934/dcds.2019133 
[8] 
Jinsen Zhuang, Yan Zhou, Yonghui Xia. Synchronization analysis of driveresponse multilayer dynamical networks with additive couplings and stochastic perturbations. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020279 
[9] 
Hua Chen, Shaohua Wu. The moving boundary problem in a chemotaxis model. Communications on Pure & Applied Analysis, 2012, 11 (2) : 735746. doi: 10.3934/cpaa.2012.11.735 
[10] 
X. Liang, Roderick S. C. Wong. On a Nested BoundaryLayer Problem. Communications on Pure & Applied Analysis, 2009, 8 (1) : 419433. doi: 10.3934/cpaa.2009.8.419 
[11] 
Jie Wang, Xiaoqiang Wang. New asymptotic analysis method for phase field models in moving boundary problem with surface tension. Discrete & Continuous Dynamical Systems  B, 2015, 20 (9) : 31853213. doi: 10.3934/dcdsb.2015.20.3185 
[12] 
Junde Wu. Bifurcation for a free boundary problem modeling the growth of necrotic multilayered tumors. Discrete & Continuous Dynamical Systems  A, 2019, 39 (6) : 33993411. doi: 10.3934/dcds.2019140 
[13] 
Liping Wang, Chunyi Zhao. Solutions with clustered bubbles and a boundary layer of an elliptic problem. Discrete & Continuous Dynamical Systems  A, 2014, 34 (5) : 23332357. doi: 10.3934/dcds.2014.34.2333 
[14] 
Liping Wang, Juncheng Wei. Solutions with interior bubble and boundary layer for an elliptic problem. Discrete & Continuous Dynamical Systems  A, 2008, 21 (1) : 333351. doi: 10.3934/dcds.2008.21.333 
[15] 
O. Guès, G. Métivier, M. Williams, K. Zumbrun. Boundary layer and long time stability for multiD viscous shocks. Discrete & Continuous Dynamical Systems  A, 2004, 11 (1) : 131160. doi: 10.3934/dcds.2004.11.131 
[16] 
Christos Sourdis. Analysis of an irregular boundary layer behavior for the steady state flow of a Boussinesq fluid. Discrete & Continuous Dynamical Systems  A, 2017, 37 (2) : 10391059. doi: 10.3934/dcds.2017043 
[17] 
Masahiro Suzuki. Asymptotic stability of a boundary layer to the EulerPoisson equations for a multicomponent plasma. Kinetic & Related Models, 2016, 9 (3) : 587603. doi: 10.3934/krm.2016008 
[18] 
Hiroshi Matsuzawa. A free boundary problem for the FisherKPP equation with a given moving boundary. Communications on Pure & Applied Analysis, 2018, 17 (5) : 18211852. doi: 10.3934/cpaa.2018087 
[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 & Continuous Dynamical Systems  B, 2020 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 & Continuous Dynamical Systems  A, 2010, 26 (2) : 737765. doi: 10.3934/dcds.2010.26.737 
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