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Global existence and comparison theorem for a nonlinear parabolic equation
Published online by Cambridge University Press: 17 April 2009
Abstract
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.
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- Copyright © Australian Mathematical Society 2003
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