Anisotropic nonlinear diffusion with absorption: existence and extinction

Alan V. Lair and Mark E. Oxley

International Journal of Mathematics and Mathematical Sciences, 1996, vol. 19, 1-8

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 .

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:347450

DOI: 10.1155/S0161171296000610

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