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Boundary dynamics of a two-dimensional 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 Yat-Sen University, Guangzhou, Guangdong 510275 |
[1] |
Shihe Xu. Analysis of a delayed free boundary problem for tumor growth. Discrete and Continuous Dynamical Systems - B, 2011, 15 (1) : 293-308. 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 and Continuous Dynamical Systems - B, 2018, 23 (6) : 2593-2605. 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 and Continuous Dynamical Systems - B, 2016, 21 (3) : 997-1008. doi: 10.3934/dcdsb.2016.21.997 |
[4] |
Shihe Xu, Meng Bai, Fangwei Zhang. Analysis of a free boundary problem for tumor growth with Gibbs-Thomson relation and time delays. Discrete and Continuous Dynamical Systems - B, 2018, 23 (9) : 3535-3551. doi: 10.3934/dcdsb.2017213 |
[5] |
Fujun Zhou, Shangbin Cui. Well-posedness and stability of a multidimensional moving boundary problem modeling the growth of tumor cord. Discrete and Continuous Dynamical Systems, 2008, 21 (3) : 929-943. 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 and Continuous Dynamical Systems, 2009, 24 (2) : 625-651. doi: 10.3934/dcds.2009.24.625 |
[7] |
Kentarou Fujie. Global asymptotic stability in a chemotaxis-growth model for tumor invasion. Discrete and Continuous Dynamical Systems - S, 2020, 13 (2) : 203-209. 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 and Continuous Dynamical Systems, 2019, 39 (5) : 2473-2510. doi: 10.3934/dcds.2019105 |
[9] |
Xiaofeng Ren. Shell structure as solution to a free boundary problem from block copolymer morphology. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 979-1003. doi: 10.3934/dcds.2009.24.979 |
[10] |
Igor Kukavica, Amjad Tuffaha. Solutions to a fluid-structure interaction free boundary problem. Discrete and Continuous Dynamical Systems, 2012, 32 (4) : 1355-1389. doi: 10.3934/dcds.2012.32.1355 |
[11] |
Jian-Guo 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 and Continuous Dynamical Systems - B, 2019, 24 (7) : 3011-3035. doi: 10.3934/dcdsb.2018297 |
[12] |
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 |
[13] |
Weiqing Xie. A free boundary problem arising from the process of Czochralski crystal growth. Conference Publications, 2001, 2001 (Special) : 380-385. doi: 10.3934/proc.2001.2001.380 |
[14] |
Jiayue Zheng, Shangbin Cui. Bifurcation analysis of a tumor-model free boundary problem with a nonlinear boundary condition. Discrete and Continuous Dynamical Systems - B, 2020, 25 (11) : 4397-4410. 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 and Continuous Dynamical Systems - B, 2017, 22 (3) : 895-911. doi: 10.3934/dcdsb.2017045 |
[16] |
Siyu Liu, Haomin Huang, Mingxin Wang. A free boundary problem for a prey-predator model with degenerate diffusion and predator-stage structure. Discrete and Continuous Dynamical Systems - B, 2020, 25 (5) : 1649-1670. 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 and Continuous Dynamical Systems - B, 2021, 26 (1) : 667-691. doi: 10.3934/dcdsb.2020084 |
[18] |
E. Camouzis, H. Kollias, I. Leventides. Stable manifold market sequences. Journal of Dynamics and Games, 2018, 5 (2) : 165-185. 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 and Continuous Dynamical Systems - B, 2020, 25 (3) : 1043-1058. doi: 10.3934/dcdsb.2019207 |
[20] |
Yuki Kaneko, Hiroshi Matsuzawa, Yoshio Yamada. A free boundary problem of nonlinear diffusion equation with positive bistable nonlinearity in high space dimensions I : Classification of asymptotic behavior. Discrete and Continuous Dynamical Systems, 2022, 42 (6) : 2719-2745. doi: 10.3934/dcds.2021209 |
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