Uniqueness and support properties of solutions to singular quasilinear parabolic equations on surfaces of revolution
Articolo
Data di Pubblicazione:
2012
Citazione:
Uniqueness and support properties of solutions to singular quasilinear parabolic equations on surfaces of revolution / F. Punzo. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 191:2(2012), pp. 311-338.
Abstract:
We study uniqueness, nonuniqueness and support properties of nonnegative bounded solutions of initial value problems on surfaces of revolution with boundary, for a class of quasilinear parabolic equations with variable density. At the boundary, the density can either vanish or diverge or need not to have a limit. In dependence of the behavior of the density near the boundary, we provide simple conditions for uniqueness or nonuniqueness of solutions; moreover, supposing that the initial datum does not intersect the boundary, we give criteria so that the support of any solution intersects the boundary at some positive time or it remains always away from it.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Porous medium equation; Singular quasilinear equations; Sub-supersolutions; Support of solutions; Well-posedness
Elenco autori:
F. Punzo
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