This paper studies the asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in ℝⁿ. Firstly, the global existence and uniqueness of classical solutions for small initial data are established. Then, we obtain the L^p, 2 ⩽ p ⩽ +℞ decay rate of solutions. The approach is based on detailed analysis of the Green function of the linearized equation with the technique of long wave-short wave decomposition and the Fourier analysis.

中文翻译：

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ℝn中非线性对流扩散反应方程的L p衰减率

本文研究的解决方案用于ℝ非线性对流扩散反应方程式的渐近行为^Ñ。首先，建立了针对小初始数据的经典解的全局存在性和唯一性。然后，我们得到大号^p，2⩽ p ⩽+℞衰变解决方案的速度。该方法基于长波-短波分解技术和傅里叶分析，对线性化方程的格林函数进行了详细分析。