Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 97, pp. 1-14.
Title: The heat equation and the shrinking
Authors: Masaki Kawagishi (Nihon University, Tokyo, Japan)
Takesi Yamanaka (Nihon University, Tokyo, Japan)
Abstract:
This article concerns the Cauchy problem for the partial
differential equation
$$
\partial_1 u(t,x)-a\partial_2^2 u(t,x)
=f(t,x,\partial_2^p u(\mu(t)t,x),\partial_2^q u(t,\nu(t)x))\,.
$$
Here $t$ and $x$ are real variables, $p$ and $q$ are positive
integers greater than 1, and the shrinking factors
$\mu(t)$, $\nu(t)$ are positive-valued functions such that
their suprema are less than 1.
Submitted April 1, 2003. Published September 17, 2003.
Math Subject Classifications: 35K05, 35K55, 35R10, 49K25.
Key Words: Partial differential equation; heat equation;
shrinking; delay; Gevrey