We study, on weighted Riemannian model manifolds, well posedness of the Cauchy problem for a class of quasilinear parabolic equations with a coefficient which can be singular at infinity. We establish uniqueness or non-uniqueness of bounded solutions, under suitable assumptions on the behavior at infinity of the singular coefficient and on the Green function for the weighted Laplace-Beltrami operator.
Uniqueness and non-uniqueness of solutions to quasilinear parabolic equations with a singular coefficient on weighted Riemannian manifolds / F. Punzo. - In: ASYMPTOTIC ANALYSIS. - ISSN 0921-7134. - 79:3-4(2012), pp. 273-301. [10.3233/ASY-2012-1098]
Uniqueness and non-uniqueness of solutions to quasilinear parabolic equations with a singular coefficient on weighted Riemannian manifolds
F. Punzo
2012
Abstract
We study, on weighted Riemannian model manifolds, well posedness of the Cauchy problem for a class of quasilinear parabolic equations with a coefficient which can be singular at infinity. We establish uniqueness or non-uniqueness of bounded solutions, under suitable assumptions on the behavior at infinity of the singular coefficient and on the Green function for the weighted Laplace-Beltrami operator.Pubblicazioni consigliate
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