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Anisotropic Nonlinear Diffusion with Absorption: Existence and Extinction

Document Type

Article

Publication Date

1996

Abstract

The authors prove that the nonlinear parabolic partial differential equation ∂ u ∂ t = ∑ i , j = 1 n ∂ 2 ∂ x i ∂ x j φ i j ( u ) − f ( u ) with homogeneous Dirichlet boundary conditions and a nonnegative initial condition has a nonnegative generalized solution u . They also give necessary and sufficient conditions on the constitutive functions φ i j and f which ensure the existence of a time t 0 > 0 for which u vanishes for all t ≥ t 0 .

Comments

Copyright © 1996 Hindawi Publishing Corporation.

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This is an open access article published by Hindawi and distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. CC BY 3.0

Reviewed at MR1386540

Source Publication

International Journal of Mathematics and Mathematical Sciences

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