A nonlinear diffusion system coupled via nonlinear boundary flux |
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Authors: | Yongsheng Mi Chunlai Mu |
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Institution: | a College of Mathematics and Physics, Chongqing University, Chongqing 400044, PR China b College of Mathematics and Computer Sciences, Yangtze Normal University, Fuling 408100, Chongqing, PR China |
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Abstract: | In this paper, we deal with the global existence and nonexistence of solutions to a nonlinear diffusion system coupled via nonlinear boundary flux. By constructing various kinds of sub- and super-solutions and using the basic properties of M-matrix, we give the necessary and sufficient conditions for global existence of nonnegative solutions. The critical curve of Fujita type is conjectured with the aid of some new results, which extend the recent results of Wang et al. Nonlinear Anal. 71 (2009) 2134-2140] and Li et al. J. Math. Anal. Appl. 340 (2008) 876-883] to more general equations. |
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Keywords: | Global existence curve Nonlinear diffusion system M-matrix Nonlinear boundary flux Blow-up |
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