非线性扩散方程Cauchy问题的临界指数

Abstract

Abstract:

In this paper, we investigate the large time behavior of solution to nonlinear diffusive equations u_t=div(|nabla u|^p-2 nabla u)+|x|^σu^q with nontrivial, nonnegative initial data. Here p>2, σ>0 and q>p-1. We prove that q_c=p-1+p+σ /N is the critical Fujita exponent. That is, if q<q_c then every positive solution blows up in finite time, but for q>q_c, there exist both global and non-global solutions to the problem. Furthermore, we establish the secondary critical exponent on the decay asymptotic behavior of an initial value at infinity.

Key words: Critical Fujita exponent, Secondary critical exponent, Nonlinear diffusive equations

CLC Number:

35K50

LI Zhong-Ping, DU Wan-Juan, MU Chun-Lai. Critical Exponents of the Cauchy Problem for Nonlinear Diffusive Equations[J].Acta mathematica scientia,Series A, 2013, 33(5): 966-976.

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Critical Exponents of the Cauchy Problem for Nonlinear Diffusive Equations

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