THE POINTWISE ESTIMATES OF SOLUTIONS FOR A NONLINEAR CONVECTION DIFFUSION REACTION EQUATION

doi:10.1016/S0252-9602(16)30117-5

摘要/Abstract

摘要：

This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension. First, the pointwise estimates of solutions are obtained, furthermore, we obtain the optimal L^p, 1≤p≤+∞, convergence rate of solutions for small initial data. Then we establish the local existence of solutions, the blow up criterion and the sufficient condition to ensure the nonnegativity of solutions for large initial data. Our approach is based on the detailed analysis of the Green function of the linearized equation and some energy estimates.

关键词: convection diffusion reaction equation, pointwise estimate, Green function, energy method

Abstract:

Key words: convection diffusion reaction equation, pointwise estimate, Green function, energy method

刘国威. THE POINTWISE ESTIMATES OF SOLUTIONS FOR A NONLINEAR CONVECTION DIFFUSION REACTION EQUATION[J]. 数学物理学报(英文版), 2017, 37(1): 79-96.

Guowei LIU. THE POINTWISE ESTIMATES OF SOLUTIONS FOR A NONLINEAR CONVECTION DIFFUSION REACTION EQUATION[J]. Acta mathematica scientia,Series B, 2017, 37(1): 79-96.

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