We investigate well-posedness of initial-boundary value problems for a class of nonlinear parabolic equations with variable density. At some part of the boundary, called singular boundary, the density can either vanish or diverge or not need to have a limit. We provide simple conditions for uniqueness or non-uniqueness of bounded solutions, depending on the behaviour of the density near the singular boundary.
Uniqueness and non-uniqueness of bounded solutions to singular nonlinear parabolic equations / F. Punzo. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 70:8(2009), pp. 3020-3029.
Uniqueness and non-uniqueness of bounded solutions to singular nonlinear parabolic equations
F. Punzo
2009
Abstract
We investigate well-posedness of initial-boundary value problems for a class of nonlinear parabolic equations with variable density. At some part of the boundary, called singular boundary, the density can either vanish or diverge or not need to have a limit. We provide simple conditions for uniqueness or non-uniqueness of bounded solutions, depending on the behaviour of the density near the singular boundary.
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