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Asymptotic behavior of solutions of a free boundary problem modelling the growth of tumors with Stokes equations
1.  Department of Mathematics, Sun YatSen University, Guangzhou, Guangdong 510275, China 
2.  Institute of Mathematics, Sun YatSen University, Guangzhou, Guangdong 510275 
[1] 
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 
[2] 
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 
[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] 
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 
[5] 
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, 2017, 22 (11) : 117. doi: 10.3934/dcdsb.2017213 
[6] 
Hantaek Bae. Solvability of the free boundary value problem of the NavierStokes equations. Discrete & Continuous Dynamical Systems  A, 2011, 29 (3) : 769801. doi: 10.3934/dcds.2011.29.769 
[7] 
Boris Muha, Zvonimir Tutek. Note on evolutionary free piston problem for Stokes equations with slip boundary conditions. Communications on Pure & Applied Analysis, 2014, 13 (4) : 16291639. doi: 10.3934/cpaa.2014.13.1629 
[8] 
Fujun Zhou, Shangbin Cui. Wellposedness and stability of a multidimensional moving boundary problem modeling the growth of tumor cord. Discrete & Continuous Dynamical Systems  A, 2008, 21 (3) : 929943. doi: 10.3934/dcds.2008.21.929 
[9] 
Zhenhua Guo, Zilai Li. Global existence of weak solution to the free boundary problem for compressible NavierStokes. Kinetic & Related Models, 2016, 9 (1) : 75103. doi: 10.3934/krm.2016.9.75 
[10] 
Zhong Tan, Leilei Tong. Asymptotic stability of stationary solutions for magnetohydrodynamic equations. Discrete & Continuous Dynamical Systems  A, 2017, 37 (6) : 34353465. doi: 10.3934/dcds.2017146 
[11] 
Feimin Huang, Xiaoding Shi, Yi Wang. Stability of viscous shock wave for compressible NavierStokes equations with free boundary. Kinetic & Related Models, 2010, 3 (3) : 409425. doi: 10.3934/krm.2010.3.409 
[12] 
Avner Friedman. Free boundary problems for systems of Stokes equations. Discrete & Continuous Dynamical Systems  B, 2016, 21 (5) : 14551468. doi: 10.3934/dcdsb.2016006 
[13] 
Xulong Qin, ZhengAn Yao. Global solutions of the free boundary problem for the compressible NavierStokes equations with densitydependent viscosity. Communications on Pure & Applied Analysis, 2010, 9 (4) : 10411052. doi: 10.3934/cpaa.2010.9.1041 
[14] 
Zilai Li, Zhenhua Guo. On free boundary problem for compressible navierstokes equations with temperaturedependent heat conductivity. Discrete & Continuous Dynamical Systems  B, 2017, 22 (10) : 39033919. doi: 10.3934/dcdsb.2017201 
[15] 
Xiaofeng Ren. Shell structure as solution to a free boundary problem from block copolymer morphology. Discrete & Continuous Dynamical Systems  A, 2009, 24 (3) : 9791003. doi: 10.3934/dcds.2009.24.979 
[16] 
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 
[17] 
Renjun Duan, Xiongfeng Yang. Stability of rarefaction wave and boundary layer for outflow problem on the twofluid NavierStokesPoisson equations. Communications on Pure & Applied Analysis, 2013, 12 (2) : 9851014. doi: 10.3934/cpaa.2013.12.985 
[18] 
Haifeng Hu, Kaijun Zhang. Stability of the stationary solution of the cauchy problem to a semiconductor full hydrodynamic model with recombinationgeneration rate. Kinetic & Related Models, 2015, 8 (1) : 117151. doi: 10.3934/krm.2015.8.117 
[19] 
Yoshikazu Giga. A remark on a Liouville problem with boundary for the Stokes and the NavierStokes equations. Discrete & Continuous Dynamical Systems  S, 2013, 6 (5) : 12771289. doi: 10.3934/dcdss.2013.6.1277 
[20] 
Toyohiko Aiki. On the existence of a weak solution to a free boundary problem for a model of a shape memory alloy spring. Discrete & Continuous Dynamical Systems  S, 2012, 5 (1) : 113. doi: 10.3934/dcdss.2012.5.1 
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