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

This is an open access article 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 http://creativecommons.org/licenses/by/3.0/

Sourced from the publisher's version of record at Hindawi: . https://doi.org/10.1155/S0161171296000610

DOI

10.1155/S0161171296000610

Source Publication

International Journal of Mathematics and Mathematical Sciences

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