ANISOTROPIC NONLINEAR DIFFUSION WITH ABSORPTION: EXISTENCE AND EXTINCTION

The authors prove that the nonlinear parabolic partial differential equation (The equation is abbreviated) 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 constituti...

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Bibliographic Details
Published inInternational Journal of Mathematics and Mathematical Sciences Vol. 1996; no. 3; pp. 427 - 434
Main Authors Lair, Alan V., Oxley, Mark E.
Format Journal Article
LanguageEnglish
Published Hindawi Limiteds 1996
Hindawi Limited
Subjects
Anisotropic nonlinear diffusion
finite extinction time
generalized solution
Anisotropic nonlinear diffusion
finite extinction time
generalized solution
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Summary:The authors prove that the nonlinear parabolic partial differential equation (The equation is abbreviated) 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_(ij) and f which ensure the existence of a time t_0＞0 for which u vanishes for all t≥t_0.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0161-1712
1687-0425
DOI:10.1155/S0161171296000610