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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] 
Mircea Sofonea, Yibin Xiao. Tykhonov wellposedness of a viscoplastic contact problem^{†}. Evolution Equations & Control Theory, 2020, 9 (4) : 11671185. doi: 10.3934/eect.2020048 
[3] 
Boling Guo, Jun Wu. Wellposedness of the initialboundary value problem for the fourthorder nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021205 
[4] 
Abraham Sylla. Influence of a slow moving vehicle on traffic: Wellposedness and approximation for a mildly nonlocal model. Networks & Heterogeneous Media, 2021, 16 (2) : 221256. doi: 10.3934/nhm.2021005 
[5] 
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 
[6] 
Iñigo U. Erneta. Wellposedness for boundary value problems for coagulationfragmentation equations. Kinetic & Related Models, 2020, 13 (4) : 815835. doi: 10.3934/krm.2020028 
[7] 
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 
[8] 
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 
[9] 
Zhaohui Huo, Boling Guo. The wellposedness of Cauchy problem for the generalized nonlinear dispersive equation. Discrete & Continuous Dynamical Systems, 2005, 12 (3) : 387402. doi: 10.3934/dcds.2005.12.387 
[10] 
Hongmei Cao, HaoGuang Li, ChaoJiang Xu, Jiang Xu. Wellposedness of Cauchy problem for Landau equation in critical Besov space. Kinetic & Related Models, 2019, 12 (4) : 829884. doi: 10.3934/krm.2019032 
[11] 
Changyan Li, Hui Li. Wellposedness of the twophase flow problem in incompressible MHD. Discrete & Continuous Dynamical Systems, 2021, 41 (12) : 56095632. doi: 10.3934/dcds.2021090 
[12] 
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 
[13] 
Xiaoqiang Dai, Shaohua Chen. Global wellposedness for the Cauchy problem of generalized Boussinesq equations in the control problem regarding initial data. Discrete & Continuous Dynamical Systems  S, 2021 doi: 10.3934/dcdss.2021114 
[14] 
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 
[15] 
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 
[16] 
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 
[17] 
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 
[18] 
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 
[19] 
Baoyan Sun, KungChien Wu. Global wellposedness and exponential stability for the fermion equation in weighted Sobolev spaces. Discrete & Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021147 
[20] 
Akram Ben Aissa. Wellposedness and direct internal stability of coupled nondegenrate Kirchhoff system via heat conduction. Discrete & Continuous Dynamical Systems  S, 2021 doi: 10.3934/dcdss.2021106 
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