Asymptotic expansions of solutions of the Cauchy problem for nonlinear parabolic equations
Asymptotic expansions of solutions of the Cauchy problem for nonlinear parabolic equations
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DOI：
10.1007/s11854-013-0038-6
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发表时间：
2012-02
期刊：
影响因子：
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通讯作者：
Kazuhiro Ishige;Tatsuki Kawakami
中科院分区：
文献类型：
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作者：
Kazuhiro Ishige;Tatsuki Kawakami
求非线性抛物方程$$ \partial_t u=\Delta u+F(x,t,u,\nabla u) \quad in \quad{\bf R}^N\times(0,\infty), \quad u(x,0)=\varphi(x)\quad in \quad{\bf R}^N, $$的柯西问题的解，并假设解的性质类似高斯核。本文在反应项和初始函数的适当假设下，建立了求解高阶渐近展开式的方法。本文是对前人研究成果的推广，所得结论适用于一类大型非线性抛物型方程。
Letbe a solution of the Cauchy problem for the nonlinear parabolic equation $$ \partial_t u=\Delta u+F(x,t,u,\nabla u) \quad in \quad{\bf R}^N\times(0,\infty), \quad u(x,0)=\varphi(x)\quad in \quad{\bf R}^N, $$ and assume that the solutionbehaves like the Gauss kernel as. In this paper, under suitable assumptions of the reaction termand the initial function, we establish the method of obtaining higher order asymptotic expansions of the solutionas. This paper is a generalization of our previous paper, and our arguments are applicable to the large class of nonlinear parabolic equations.