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Wellposedness and stability of a multidimensional moving boundary problem modeling the growth of tumor cord
1.  Department of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, China 
2.  Institute of Mathematics, Sun YatSen University, Guangzhou, Guangdong 510275, China 
[1] 
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 
[2] 
Barbara Kaltenbacher, Irena Lasiecka. Wellposedness of the Westervelt and the Kuznetsov equation with nonhomogeneous Neumann boundary conditions. Conference Publications, 2011, 2011 (Special) : 763773. doi: 10.3934/proc.2011.2011.763 
[3] 
George Avalos, Pelin G. Geredeli, Justin T. Webster. Semigroup wellposedness of a linearized, compressible fluid with an elastic boundary. Discrete & Continuous Dynamical Systems  B, 2018, 23 (3) : 12671295. doi: 10.3934/dcdsb.2018151 
[4] 
Ivonne Rivas, Muhammad Usman, BingYu Zhang. Global wellposedness and asymptotic behavior of a class of initialboundaryvalue problem of the KortewegDe Vries equation on a finite domain. Mathematical Control & Related Fields, 2011, 1 (1) : 6181. doi: 10.3934/mcrf.2011.1.61 
[5] 
Zhaohui Huo, Boling Guo. The wellposedness of Cauchy problem for the generalized nonlinear dispersive equation. Discrete & Continuous Dynamical Systems  A, 2005, 12 (3) : 387402. doi: 10.3934/dcds.2005.12.387 
[6] 
Janet Dyson, Rosanna VillellaBressan, G. F. Webb. The evolution of a tumor cord cell population. Communications on Pure & Applied Analysis, 2004, 3 (3) : 331352. doi: 10.3934/cpaa.2004.3.331 
[7] 
K. Domelevo. Wellposedness of a kinetic model of dispersed twophase flow with pointparticles and stability of travelling waves. Discrete & Continuous Dynamical Systems  B, 2002, 2 (4) : 591607. doi: 10.3934/dcdsb.2002.2.591 
[8] 
Stefan Meyer, Mathias Wilke. Global wellposedness and exponential stability for Kuznetsov's equation in $L_p$spaces. Evolution Equations & Control Theory, 2013, 2 (2) : 365378. doi: 10.3934/eect.2013.2.365 
[9] 
Aissa Guesmia, Nassereddine Tatar. Some wellposedness and stability results for abstract hyperbolic equations with infinite memory and distributed time delay. Communications on Pure & Applied Analysis, 2015, 14 (2) : 457491. doi: 10.3934/cpaa.2015.14.457 
[10] 
Ahmed Bchatnia, Aissa Guesmia. Wellposedness and asymptotic stability for the Lamé system with infinite memories in a bounded domain. Mathematical Control & Related Fields, 2014, 4 (4) : 451463. doi: 10.3934/mcrf.2014.4.451 
[11] 
Jiang Xu. Wellposedness and stability of classical solutions to the multidimensional full hydrodynamic model for semiconductors. Communications on Pure & Applied Analysis, 2009, 8 (3) : 10731092. doi: 10.3934/cpaa.2009.8.1073 
[12] 
Kenji Nakanishi, Hideo Takaoka, Yoshio Tsutsumi. Local wellposedness in low regularity of the MKDV equation with periodic boundary condition. Discrete & Continuous Dynamical Systems  A, 2010, 28 (4) : 16351654. doi: 10.3934/dcds.2010.28.1635 
[13] 
Maxim A. Olshanskii, Leo G. Rebholz, Abner J. Salgado. On wellposedness of a velocityvorticity formulation of the stationary NavierStokes equations with noslip boundary conditions. Discrete & Continuous Dynamical Systems  A, 2018, 38 (7) : 34593477. doi: 10.3934/dcds.2018148 
[14] 
Vishal Vasan, Bernard Deconinck. Wellposedness of boundaryvalue problems for the linear BenjaminBonaMahony equation. Discrete & Continuous Dynamical Systems  A, 2013, 33 (7) : 31713188. doi: 10.3934/dcds.2013.33.3171 
[15] 
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 
[16] 
Yuanyuan Ren, Yongsheng Li, Wei Yan. Sharp wellposedness of the Cauchy problem for the fourth order nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2018, 17 (2) : 487504. doi: 10.3934/cpaa.2018027 
[17] 
Changxing Miao, Bo Zhang. Global wellposedness of the Cauchy problem for nonlinear Schrödingertype equations. Discrete & Continuous Dynamical Systems  A, 2007, 17 (1) : 181200. doi: 10.3934/dcds.2007.17.181 
[18] 
Shinya Kinoshita. Wellposedness for the Cauchy problem of the KleinGordonZakharov system in 2D. Discrete & Continuous Dynamical Systems  A, 2018, 38 (3) : 14791504. doi: 10.3934/dcds.2018061 
[19] 
Nobu Kishimoto. Local wellposedness for the Cauchy problem of the quadratic Schrödinger equation with nonlinearity $\bar u^2$. Communications on Pure & Applied Analysis, 2008, 7 (5) : 11231143. doi: 10.3934/cpaa.2008.7.1123 
[20] 
Yuri Trakhinin. On wellposedness of the plasmavacuum interface problem: the case of nonelliptic interface symbol. Communications on Pure & Applied Analysis, 2016, 15 (4) : 13711399. doi: 10.3934/cpaa.2016.15.1371 
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