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.