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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] 
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 
[3] 
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 
[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  A, 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  A, 2009, 24 (2) : 625651. doi: 10.3934/dcds.2009.24.625 
[7] 
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 
[8] 
Igor Kukavica, Amjad Tuffaha. Solutions to a fluidstructure interaction free boundary problem. Discrete & Continuous Dynamical Systems  A, 2012, 32 (4) : 13551389. doi: 10.3934/dcds.2012.32.1355 
[9] 
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 
[10] 
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 
[11] 
E. Camouzis, H. Kollias, I. Leventides. Stable manifold market sequences. Journal of Dynamics & Games, 2018, 5 (2) : 165185. doi: 10.3934/jdg.2018010 
[12] 
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 
[13] 
Toyohiko Aiki. A free boundary problem for an elastic material. Conference Publications, 2007, 2007 (Special) : 1017. doi: 10.3934/proc.2007.2007.10 
[14] 
Jian Yang. Asymptotic behavior of solutions for competitive models with a free boundary. Discrete & Continuous Dynamical Systems  A, 2015, 35 (7) : 32533276. doi: 10.3934/dcds.2015.35.3253 
[15] 
Hayk Mikayelyan, Henrik Shahgholian. Convexity of the free boundary for an exterior free boundary problem involving the perimeter. Communications on Pure & Applied Analysis, 2013, 12 (3) : 14311443. doi: 10.3934/cpaa.2013.12.1431 
[16] 
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 
[17] 
Alfonso C. Casal, Jesús Ildefonso Díaz, José M. Vegas. Finite extinction time property for a delayed linear problem on a manifold without boundary. Conference Publications, 2011, 2011 (Special) : 265271. doi: 10.3934/proc.2011.2011.265 
[18] 
Antonios Zagaris, Christophe Vandekerckhove, C. William Gear, Tasso J. Kaper, Ioannis G. Kevrekidis. Stability and stabilization of the constrained runs schemes for equationfree projection to a slow manifold. Discrete & Continuous Dynamical Systems  A, 2012, 32 (8) : 27592803. doi: 10.3934/dcds.2012.32.2759 
[19] 
Eric Benoît. Bifurcation delay  the case of the sequence: Stable focus  unstable focus  unstable node. Discrete & Continuous Dynamical Systems  S, 2009, 2 (4) : 911929. doi: 10.3934/dcdss.2009.2.911 
[20] 
Xiaoshan Chen, Fahuai Yi. Free boundary problem of Barenblatt equation in stochastic control. Discrete & Continuous Dynamical Systems  B, 2016, 21 (5) : 14211434. doi: 10.3934/dcdsb.2016003 
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