Blow-up Rate and Profile for a Class of Quasilinear Parabolic System
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摘要: 研究了一类非局部退化拟线性抛物型方程组,在齐次Dirichlet边界条件下的正解,在参数和初始数据满足一定的条件下,得到了解的爆破率和爆破模式.Abstract: The positive solutions to a class of nonlocal and degenerate quasilinear parabolic system with null Dirichlet boundary conditions are dealt with.The blow-up rate and blow-up profile were gained if the parameters and the initial data satisfy some conditions.
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Key words:
- degenerate parabolic system /
- nonlocal sources /
- blow-up rate /
- blow-up profile
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[1] Friedman A,Mcleod B. Blow-up of positive solutions of semilinear heat equations[J]. Indiana Univ Math J,1985,34(2):425-447. doi: 10.1512/iumj.1985.34.34025 [2] Furter J, Grinfeld M. Local vs non-local interactions in population dynamics[J].J Math Biology,1989,27(1):65-80. doi: 10.1007/BF00276081 [3] LU Hui-hua, WANG Ming-xin. Global solutions and blow-up problems for a nonlinear degenerate parabolic system coupled via nonlocal sources[J].J Math Anal Appl, 2007, 333(2):984-1007. doi: 10.1016/j.jmaa.2006.11.023 [4] ZHENG Si-ning, WANG Li-dong. Blow-up rate and profile for a degenerate parabolic system coupled via nonlocal sources[J].Comput Math Appl,2006,52(10/11):1387-1402. doi: 10.1016/j.camwa.2006.10.018 [5] DENG Wei-bin, LI Yu-xiang, XIE Cun-hong. Blow-up and global existence for a nonlocal degenerate parabolic system[J].J Math Anal Appl,2003,277(1):199-217. doi: 10.1016/S0022-247X(02)00533-4 [6] DUAN Zhi-wen, DENG Wei-bin, XIE Chun-hong. Uniform blow-up profile for a degenerate parabolic system with nonlocal source[J].Computers and Mathematics With Applications,2004,47(6/7):977-995. doi: 10.1016/S0898-1221(04)90081-8 [7] LIU Qi-lin, LI Yu-xiang, GAO Hong-jun. Uniform blow-up rate for a nonlocal degenerate parabolic equations[J].Nonlinear Analysis,2007,66(4):881-889. doi: 10.1016/j.na.2005.12.029 [8] Souplet P. Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source[J].J Differential Equations,1999, 153(2):374-406. doi: 10.1006/jdeq.1998.3535 [9] DU Li-li. Blow-up for a degenerate reaction-diffusion system with nonlinear localized sources[J].J Math Anal Appl,2006,324(1):304-320. doi: 10.1016/j.jmaa.2005.11.052 -
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