Electron. J. Diff. Eqns., Vol. 2005(2005), No. 113, pp. 1-14.

Vanishing of solutions of diffusion equation with convection and absorption

Alexander Gladkov, Sergey Prokhozhy

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.

Show me the PDF file (314K), TEX file, and other files for this article.

Alexander Gladkov
Mathematics Department, Vitebsk State University
Moskovskii pr. 33, 210038 Vitebsk, Belarus
email: gladkov@vsu.by
Sergey Prokhozhy
Mathematics Department, Vitebsk State University
Moskovskii Pr. 33, 210038 Vitebsk, Belarus
email: prokhozhy@vsu.by

Return to the EJDE web page