\(L^p\) decay rate for a nonlinear convection diffusion reaction equation in \(\mathbb{R}^n\). (English) Zbl 1464.35241
Summary: This paper studies the asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in \(\mathbb{R}^n\). Firstly, the global existence and uniqueness of classical solutions for small initial data are established. Then, we obtain the \(L^p\), \(2\leq p\leq+\infty\) 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.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35A09 | Classical solutions to PDEs |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
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