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.

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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

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