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. ©2012-IOS Press and the authors. All rights reserved.
Uniqueness and non-uniqueness of solutions to quasilinear parabolic equations with a singular coefficient on weighted Riemannian manifolds
PUNZO, FABIO
2012-01-01
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. ©2012-IOS Press and the authors. All rights reserved.File in questo prodotto:
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