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Blowup behavior for a quasilinear parabolic equation with nonlinear boundary condition
1.  Department of Mathematics, National Taiwan Normal University, 88, S4 Ting Chou Road, Taipei 116, Taiwan 
[1] 
Bendong Lou. Selfsimilar solutions in a sector for a quasilinear parabolic equation. Networks & Heterogeneous Media, 2012, 7 (4) : 857879. doi: 10.3934/nhm.2012.7.857 
[2] 
Zhiqing Liu, Zhong Bo Fang. Blowup phenomena for a nonlocal quasilinear parabolic equation with timedependent coefficients under nonlinear boundary flux. Discrete & Continuous Dynamical Systems  B, 2016, 21 (10) : 36193635. doi: 10.3934/dcdsb.2016113 
[3] 
Thomas Y. Hou, Ruo Li. Nonexistence of locally selfsimilar blowup for the 3D incompressible NavierStokes equations. Discrete & Continuous Dynamical Systems  A, 2007, 18 (4) : 637642. doi: 10.3934/dcds.2007.18.637 
[4] 
Mingyou Zhang, Qingsong Zhao, Yu Liu, Wenke Li. Finite time blowup and global existence of solutions for semilinear parabolic equations with nonlinear dynamical boundary condition. Electronic Research Archive, 2020, 28 (1) : 369381. doi: 10.3934/era.2020021 
[5] 
Alexander Gladkov. Blowup problem for semilinear heat equation with nonlinear nonlocal Neumann boundary condition. Communications on Pure & Applied Analysis, 2017, 16 (6) : 20532068. doi: 10.3934/cpaa.2017101 
[6] 
Keng Deng, Zhihua Dong. Blowup for the heat equation with a general memory boundary condition. Communications on Pure & Applied Analysis, 2012, 11 (5) : 21472156. doi: 10.3934/cpaa.2012.11.2147 
[7] 
Shota Sato, Eiji Yanagida. Singular backward selfsimilar solutions of a semilinear parabolic equation. Discrete & Continuous Dynamical Systems  S, 2011, 4 (4) : 897906. doi: 10.3934/dcdss.2011.4.897 
[8] 
Shota Sato, Eiji Yanagida. Forward selfsimilar solution with a moving singularity for a semilinear parabolic equation. Discrete & Continuous Dynamical Systems  A, 2010, 26 (1) : 313331. doi: 10.3934/dcds.2010.26.313 
[9] 
Marek Fila, Michael Winkler, Eiji Yanagida. Convergence to selfsimilar solutions for a semilinear parabolic equation. Discrete & Continuous Dynamical Systems  A, 2008, 21 (3) : 703716. doi: 10.3934/dcds.2008.21.703 
[10] 
Pavol Quittner, Philippe Souplet. Blowup rate of solutions of parabolic poblems with nonlinear boundary conditions. Discrete & Continuous Dynamical Systems  S, 2012, 5 (3) : 671681. doi: 10.3934/dcdss.2012.5.671 
[11] 
C. Brändle, F. Quirós, Julio D. Rossi. Nonsimultaneous blowup for a quasilinear parabolic system with reaction at the boundary. Communications on Pure & Applied Analysis, 2005, 4 (3) : 523536. doi: 10.3934/cpaa.2005.4.523 
[12] 
Victor A. Galaktionov, JuanLuis Vázquez. The problem Of blowup in nonlinear parabolic equations. Discrete & Continuous Dynamical Systems  A, 2002, 8 (2) : 399433. doi: 10.3934/dcds.2002.8.399 
[13] 
Marco Cannone, Grzegorz Karch. On selfsimilar solutions to the homogeneous Boltzmann equation. Kinetic & Related Models, 2013, 6 (4) : 801808. doi: 10.3934/krm.2013.6.801 
[14] 
Shouming Zhou, Chunlai Mu, Yongsheng Mi, Fuchen Zhang. Blowup for a nonlocal diffusion equation with exponential reaction term and Neumann boundary condition. Communications on Pure & Applied Analysis, 2013, 12 (6) : 29352946. doi: 10.3934/cpaa.2013.12.2935 
[15] 
Xiaoqiang Dai, Chao Yang, Shaobin Huang, Tao Yu, Yuanran Zhu. Finite time blowup for a wave equation with dynamic boundary condition at critical and high energy levels in control systems. Electronic Research Archive, 2020, 28 (1) : 91102. doi: 10.3934/era.2020006 
[16] 
Yoshikazu Giga. Interior derivative blowup for quasilinear parabolic equations. Discrete & Continuous Dynamical Systems  A, 1995, 1 (3) : 449461. doi: 10.3934/dcds.1995.1.449 
[17] 
L. Olsen. Rates of convergence towards the boundary of a selfsimilar set. Discrete & Continuous Dynamical Systems  A, 2007, 19 (4) : 799811. doi: 10.3934/dcds.2007.19.799 
[18] 
Monica Marras, Stella Vernier Piro. Bounds for blowup time in nonlinear parabolic systems. Conference Publications, 2011, 2011 (Special) : 10251031. doi: 10.3934/proc.2011.2011.1025 
[19] 
Huiling Li, Mingxin Wang. Properties of blowup solutions to a parabolic system with nonlinear localized terms. Discrete & Continuous Dynamical Systems  A, 2005, 13 (3) : 683700. doi: 10.3934/dcds.2005.13.683 
[20] 
Hyungjin Huh. Selfsimilar solutions to nonlinear Dirac equations and an application to nonuniqueness. Evolution Equations & Control Theory, 2018, 7 (1) : 5360. doi: 10.3934/eect.2018003 
2018 Impact Factor: 1.143
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