Large time asymptotics for fundamental solutions of diffusion equations
This paper gives asymptotic estimates for U(x,y,t) which is the fundamental solution for the parabolic operator \[ \partial /\partial t- \sum^{n}_{j,k=1}a_{jk}(x)\partial^ 2/\partial x_ j\partial x_ k+\sum^{n}_{j=1}b_ j(x)\partial /\partial x_ j+c(x),\quad x\in {\mathbb{R}}^ n,\quad t>0. \] These estimates are for large values of t. Specific estimates are given for these asymptotic forms which involve negative powers of t (for n odd) and negative powers of t multiplied by positive powers of log t (for n even). The cases c(x)\(\equiv 0\), \(c(x)<0\), \(c(x)>0\) are discussed separately.
scientific article; zbMATH DE number 3944393