The pointwise estimates of solutions for a nonlinear convection diffusion reaction equation

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• 关键词：convection diffusion reaction equation ; pointwise estimate ; Green function ; energy method
• 刊名：Acta Mathematica Scientia
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：37
• 期：1
• 页码：79-96
• 全文大小：232 K
• 卷排序：37

文摘

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 Lp, 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.