Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 67, pp. 1-22.

Title: Singular solutions of doubly singular 
       parabolic equations with absorption

Authors: Yuanwei Qi (Hong Kong Univ. of Science & Technology, Hong Kong)
         Mingxin Wang (Southeast University, Nanjing, China)
         
Abstract: 
 In this paper we study a doubly singular parabolic equation with 
 absorption, 
 $$ u_t = \hbox{\rm div} ( |\nabla u^m|^{p-2}\nabla u^m ) -u^q
 $$
 with $m>0$, $p>1$, $m(p-1)<1$, and $q>1$. 
 We give a complete classification of solutions, which we call singular,
 that are non-negative, non-trivial, continuous in 
 ${\mathbb R}^n \times [0, \infty)\backslash\{(0,0)\} $, 
 and satisfy $u(x,0)=0$ for all $x\neq 0$. 
 Applications of similar but simpler equations show that these solutions
 are very important in the study of intermediate asymptotic behavior of 
 general solutions.

Submitted July 15, 2000. Published November 8, 2000.
Math Subject Classifications: 35K65, 35K15.
Key Words: doubly singular parabolic equation; absorption; singular solutions.