The heat equation and the shrinking

Electronic Journal of Differential Equations

关键词: Partial differential equation;    heat equation;    shrinking;    delay;    Gevrey;   

DOI  :  

来源: DOAJ

【 摘 要 】

This article concerns the Cauchy problem for the partial differential equation $$ partial_1 u(t,x)-apartial_2^2 u(t,x) =f(t,x,partial_2^p u(mu(t)t,x),partial_2^q u(t, u(t)x)),. $$ Here $t$ and $x$ are real variables, $p$ and $q$ are positive integers greater than 1, and the shrinking factors $mu(t)$, $ u(t)$ are positive-valued functions such that their suprema are less than 1.

【 授权许可】

Unknown