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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  and
Abbas Moameni
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
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 3 , June 2003 , pp. 481 - 492
Copyright
Copyright © Australian Mathematical Society 2003

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