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Asymptotic behavior of solutions for parabolic differential equations with invariance and applications to a free boundary problem modeling tumor growth
Boundary dynamics of a twodimensional diffusive free boundary problem
1.  Mathematics and Computer Science Department, Goucher College, 1021 Dulaney Valley Road, Baltimore, MD, 21204, United States 
2.  Department of Mathematics, University of California, Irvine, CA 926973875 
[1] 
Wenming Hu, Huicheng Yin. Wellposedness of low regularity solutions to the second order strictly hyperbolic equations with nonLipschitzian coefficients. Communications on Pure & Applied Analysis, 2019, 18 (4) : 18911919. doi: 10.3934/cpaa.2019088 
[2] 
Kenji Nakanishi, Hideo Takaoka, Yoshio Tsutsumi. Local wellposedness in low regularity of the MKDV equation with periodic boundary condition. Discrete & Continuous Dynamical Systems  A, 2010, 28 (4) : 16351654. doi: 10.3934/dcds.2010.28.1635 
[3] 
Lars Diening, Michael Růžička. An existence result for nonNewtonian fluids in nonregular domains. Discrete & Continuous Dynamical Systems  S, 2010, 3 (2) : 255268. doi: 10.3934/dcdss.2010.3.255 
[4] 
Yuri Trakhinin. On wellposedness of the plasmavacuum interface problem: the case of nonelliptic interface symbol. Communications on Pure & Applied Analysis, 2016, 15 (4) : 13711399. doi: 10.3934/cpaa.2016.15.1371 
[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] 
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 
[7] 
Ugur G. Abdulla. On the optimal control of the free boundary problems for the second order parabolic equations. I. Wellposedness and convergence of the method of lines. Inverse Problems & Imaging, 2013, 7 (2) : 307340. doi: 10.3934/ipi.2013.7.307 
[8] 
Takamori Kato. Global wellposedness for the Kawahara equation with low regularity. Communications on Pure & Applied Analysis, 2013, 12 (3) : 13211339. doi: 10.3934/cpaa.2013.12.1321 
[9] 
Hyungjin Huh, Bora Moon. Low regularity wellposedness for GrossNeveu equations. Communications on Pure & Applied Analysis, 2015, 14 (5) : 19031913. doi: 10.3934/cpaa.2015.14.1903 
[10] 
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 
[11] 
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 
[12] 
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 
[13] 
Zhaohui Huo, Boling Guo. The wellposedness of Cauchy problem for the generalized nonlinear dispersive equation. Discrete & Continuous Dynamical Systems  A, 2005, 12 (3) : 387402. doi: 10.3934/dcds.2005.12.387 
[14] 
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 
[15] 
Yoshihiro Shibata. Global wellposedness of unsteady motion of viscous incompressible capillary liquid bounded by a free surface. Evolution Equations & Control Theory, 2018, 7 (1) : 117152. doi: 10.3934/eect.2018007 
[16] 
Daniel Coutand, Steve Shkoller. A simple proof of wellposedness for the freesurface incompressible Euler equations. Discrete & Continuous Dynamical Systems  S, 2010, 3 (3) : 429449. doi: 10.3934/dcdss.2010.3.429 
[17] 
Yoshihiro Shibata. Local wellposedness of free surface problems for the NavierStokes equations in a general domain. Discrete & Continuous Dynamical Systems  S, 2016, 9 (1) : 315342. doi: 10.3934/dcdss.2016.9.315 
[18] 
Hiroyuki Hirayama, Mamoru Okamoto. Wellposedness and scattering for fourth order nonlinear Schrödinger type equations at the scaling critical regularity. Communications on Pure & Applied Analysis, 2016, 15 (3) : 831851. doi: 10.3934/cpaa.2016.15.831 
[19] 
Magdalena Czubak, Nina Pikula. Low regularity wellposedness for the 2D MaxwellKleinGordon equation in the Coulomb gauge. Communications on Pure & Applied Analysis, 2014, 13 (4) : 16691683. doi: 10.3934/cpaa.2014.13.1669 
[20] 
Takafumi Akahori. Low regularity global wellposedness for the nonlinear Schrödinger equation on closed manifolds. Communications on Pure & Applied Analysis, 2010, 9 (2) : 261280. doi: 10.3934/cpaa.2010.9.261 
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