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Global existence and comparison theorem for a nonlinear parabolic equation

Published online by Cambridge University Press:  17 April 2009

Mahmoud Hesaaraki
Affiliation:
Department of Mathematics, Sharif University of Technology, P.O. Box 11365–9415, Tehran, Iran, e-mail: hesaraki@sina.sharif.ac.ir, moameni@mehr.sharif.ac.ir
Abbas Moameni
Affiliation:
Department of Mathematics, Sharif University of Technology, P.O. Box 11365–9415, Tehran, Iran, e-mail: hesaraki@sina.sharif.ac.ir, moameni@mehr.sharif.ac.ir
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Abstract

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In this paper we consider a nonlinear parabolic equation with gradient dependent nonlinearities of the form

0 < p, q and a, b ∈ ℝ, with homogeneous boundary condition in a bounded domain Ω ⊆ ℝ,N. In the case 0 < p, q ≤ 1 we prove the existence of solution for suitable initial data. A comparison theorem for the solutions with respect to supersoultions and subsolutions is proved. Using these result, uniqueness and boundedness of solutions is studied.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2003

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