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Boundary dynamics of a twodimensional diffusive free boundary problem
Asymptotic behavior of solutions for parabolic differential equations with invariance and applications to a free boundary problem modeling tumor growth
1.  Department of Mathematics, Suzhou University, Suzhou, Jiangsu 215006, China 
2.  Department of Mathematics, Sun YatSen University, Guangzhou, Guangdong 510275 
[1] 
Shihe Xu. Analysis of a delayed free boundary problem for tumor growth. Discrete & Continuous Dynamical Systems  B, 2011, 15 (1) : 293308. doi: 10.3934/dcdsb.2011.15.293 
[2] 
Zejia Wang, Suzhen Xu, Huijuan Song. Stationary solutions of a free boundary problem modeling growth of angiogenesis tumor with inhibitor. Discrete & Continuous Dynamical Systems  B, 2018, 23 (6) : 25932605. doi: 10.3934/dcdsb.2018129 
[3] 
Shihe Xu, Yinhui Chen, Meng Bai. Analysis of a free boundary problem for avascular tumor growth with a periodic supply of nutrients. Discrete & Continuous Dynamical Systems  B, 2016, 21 (3) : 9971008. doi: 10.3934/dcdsb.2016.21.997 
[4] 
Shihe Xu, Meng Bai, Fangwei Zhang. Analysis of a free boundary problem for tumor growth with GibbsThomson relation and time delays. Discrete & Continuous Dynamical Systems  B, 2018, 23 (9) : 35353551. doi: 10.3934/dcdsb.2017213 
[5] 
Fujun Zhou, Shangbin Cui. Wellposedness and stability of a multidimensional moving boundary problem modeling the growth of tumor cord. Discrete & Continuous Dynamical Systems, 2008, 21 (3) : 929943. doi: 10.3934/dcds.2008.21.929 
[6] 
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, 2009, 24 (2) : 625651. doi: 10.3934/dcds.2009.24.625 
[7] 
Kentarou Fujie. Global asymptotic stability in a chemotaxisgrowth model for tumor invasion. Discrete & Continuous Dynamical Systems  S, 2020, 13 (2) : 203209. doi: 10.3934/dcdss.2020011 
[8] 
Yaodan Huang, Zhengce Zhang, Bei Hu. Bifurcation from stability to instability for a free boundary tumor model with angiogenesis. Discrete & Continuous Dynamical Systems, 2019, 39 (5) : 24732510. doi: 10.3934/dcds.2019105 
[9] 
Xiaofeng Ren. Shell structure as solution to a free boundary problem from block copolymer morphology. Discrete & Continuous Dynamical Systems, 2009, 24 (3) : 9791003. doi: 10.3934/dcds.2009.24.979 
[10] 
Igor Kukavica, Amjad Tuffaha. Solutions to a fluidstructure interaction free boundary problem. Discrete & Continuous Dynamical Systems, 2012, 32 (4) : 13551389. doi: 10.3934/dcds.2012.32.1355 
[11] 
JianGuo Liu, Min Tang, Li Wang, Zhennan Zhou. Analysis and computation of some tumor growth models with nutrient: From cell density models to free boundary dynamics. Discrete & Continuous Dynamical Systems  B, 2019, 24 (7) : 30113035. doi: 10.3934/dcdsb.2018297 
[12] 
Junde Wu. Bifurcation for a free boundary problem modeling the growth of necrotic multilayered tumors. Discrete & Continuous Dynamical Systems, 2019, 39 (6) : 33993411. doi: 10.3934/dcds.2019140 
[13] 
Weiqing Xie. A free boundary problem arising from the process of Czochralski crystal growth. Conference Publications, 2001, 2001 (Special) : 380385. doi: 10.3934/proc.2001.2001.380 
[14] 
Jiayue Zheng, Shangbin Cui. Bifurcation analysis of a tumormodel free boundary problem with a nonlinear boundary condition. Discrete & Continuous Dynamical Systems  B, 2020, 25 (11) : 43974410. doi: 10.3934/dcdsb.2020103 
[15] 
Chengxia Lei, Yihong Du. Asymptotic profile of the solution to a free boundary problem arising in a shifting climate model. Discrete & Continuous Dynamical Systems  B, 2017, 22 (3) : 895911. doi: 10.3934/dcdsb.2017045 
[16] 
Siyu Liu, Haomin Huang, Mingxin Wang. A free boundary problem for a preypredator model with degenerate diffusion and predatorstage structure. Discrete & Continuous Dynamical Systems  B, 2020, 25 (5) : 16491670. doi: 10.3934/dcdsb.2019245 
[17] 
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, 2021, 26 (1) : 667691. doi: 10.3934/dcdsb.2020084 
[18] 
E. Camouzis, H. Kollias, I. Leventides. Stable manifold market sequences. Journal of Dynamics & Games, 2018, 5 (2) : 165185. doi: 10.3934/jdg.2018010 
[19] 
Yuan Wu, Jin Liang, Bei Hu. A free boundary problem for defaultable corporate bond with credit rating migration risk and its asymptotic behavior. Discrete & Continuous Dynamical Systems  B, 2020, 25 (3) : 10431058. doi: 10.3934/dcdsb.2019207 
[20] 
Fujun Zhou, Junde Wu, Shangbin Cui. Existence and asymptotic behavior of solutions to a moving boundary problem modeling the growth of multilayer tumors. Communications on Pure & Applied Analysis, 2009, 8 (5) : 16691688. doi: 10.3934/cpaa.2009.8.1669 
2020 Impact Factor: 1.392
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