Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 113, pp. 1-14.

Title: Vanishing of solutions of diffusion equation with
convection and absorption

Authors: Alexander Gladkov (Vitebsk State Univ., Belarus)
         Sergey Prokhozhy  (Vitebsk State Univ., Belarus)

Abstract: 
 We study the vanishing of solutions of the Cauchy problem for
  the equation
 $$
 u_t = \sum_{i,j=1}^N a_{ij}(u^m)_{x_ix_j} + \sum_{i=1}^N
 b_i(u^n)_{x_i} - cu^p, \quad (x,t)\in S = \mathbb{R}^N\times(0,+\infty).
 $$
 Obtained results depend on relations of parameters
 of the problem and growth of initial data at infinity.
  
Submitted June 10, 2005. Published October 17, 2005.
Math Subject Classifications: 35K55, 35K65.
Key Words: Diffusion equation; vanishing of solutions.