Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 53, pp. 1-12.
Title: Qualitative properties of solutions to semilinear
heat equations with singular initial data
Author: Junjie Li (Zhejiang University, China)
Abstract:
This article concerns the nonnegative solutions to the Cauchy problem
$$\displaylines{
u_t - \Delta u + b(x,t)|u|^{p-1}u = 0 \quad \hbox{in }
\mathbb{R}^N \times (0,{\infty}), \cr
u(x,0) = u_0(x) \quad \mbox{in } \mathbb{R}^N \,.
}$$
We investigate how the comparison principle, extinction
in finite time, instantaneous shrinking of support,
and existence of solutions depend on the behaviour of
the coefficient $b(x,t)$.
Submitted December 5, 2002. Published April 8, 2004.
Math Subject Classifications: 35B05, 35K55.
Key Words: Comparison principle; extinction; shrinking of support;
existence.