Abstract
This paper deals with positive solutions to a class of nonlocal and degenerate quasilinear parabolic system with null Dirichlet boundary conditions. The blow-up rate and blow-up profile are gained if the parameters and the initial data satisfy some conditions.
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Friedman, A. and Mcleod, B. Blow-up of positive solutions of semilinear heat equations. Indiana Univ. Math. J. 34(2), 425–447 (1985)
Furter, J. and Grinfeld, M. Local vs. non-local interactions in population dynamics. J. Math. Biology 27(1), 65–80 (1989)
Li, Huilin and Wang, Mingxin. Global solutions and blow-up problems for a nonlinear degenerate parabolic system coupled via nonlocal sources. J. Math. Anal. Appl. 333(2), 984–1007 (2007)
Zheng, Sining and Wang, Lidong. Blow-up rate and profile for a degenerate parabolic system coupled via nonlocal sources. Comput. Math. Appl. 52(10–11), 1387–1402 (2006)
Deng, Weibing, Li, Yuxiang, and Xie, Chunhong. Blow-up and global existence for a nonlocal degenerate parabolic system. J. Math. Anal. Appl. 277(1), 199–217 (2003)
Chen, Yujuan. Blow-up and global existence for a nonlocal degenerate quasilinear parabolic system. Acta Mathematica Scientia (Series A) (in preprint)
Duan, Zhiwen, Deng, Weibing, and Xie, Chunhong. Uniform blow-up profile for a degenerate parabolic system with nonlocal source. Comput. Math. with Appl. 47(6–7), 977–995 (2004)
Liu, Qilin, Li, Yuxiang, and Gao, Hongjun. Uniform blow-up rate for a nonlocal degenerate parabolic equations. Nonlinear Analysis 66(4), 881–889 (2007)
Souplet, P. Uniform blow-up profiles and boundary behavior for diffusion equations with non-local nonlinear source. J. Diff. Eqns. 153(2), 374–406 (1999)
Du, Lili. Blow-up for a degenerate reaction-diffusion system with nonlinear localized sources. J. Math. Anal. Appl. 324(1), 304–320 (2006)
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Communicated by Xing-ming GUO
Project supported by the National Natural Science Foundation of China (No. 10671210), the Foundation of Jiangsu Education Commission (No. 07KJD110166), the Postdoctoral Research Foundation of Jiangsu Province (No. 0702004C), and the Project of Nantong University (Nos. 06Z011, 08B02)
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Chen, Yj., Zhu, Yp. Blow-up rate and profile for a class of quasilinear parabolic system. Appl. Math. Mech.-Engl. Ed. 30, 865–874 (2009). https://doi.org/10.1007/s10483-009-0706-y
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DOI: https://doi.org/10.1007/s10483-009-0706-y