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Optimal existence and uniqueness in a nonlinear diffusion–absorption equation with critical exponents

Published online by Cambridge University Press:  14 November 2011

M. Chaves ,
J. L. Vazquez  and
M. Walias
M. Chaves
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
J. L. Vazquez
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
M. Walias
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
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Abstract

We study the existence and uniqueness of non-negative solutions of the nonlinear parabolic equation

posed in Q = RN × (0, ∞) with general initial data u(x, 0) = u0(x) ≧ 0. We find optimal exponential growth conditions for existence of solutions. Similar conditions apply for uniqueness, but the growth rate is different. Such conditions strongly depart from the linear case m = 1, ut = Δu – u, and also from the purely diffusive case ut = Δum.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 2 , 1997 , pp. 217 - 242
Copyright
Copyright © Royal Society of Edinburgh 1997

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