Uniqueness and non-uniqueness of solutions to quasilinear parabolic equations with a singular coefficient on weighted Riemannian manifolds

被引：8
|
作者：
Punzo, Fabio [1 ]
机构：
[1] Univ Roma La Sapienza, Dipartimento Matemat G Castelnuovo, I-00185 Rome, Italy
来源：
ASYMPTOTIC ANALYSIS | 2012年 / 79卷 / 3-4期
关键词：
singular non-linear parabolic equations; weighted Riemannian manifolds; weighted Laplace-Beltrami operator; well-posedness; sub-supersolutions;
D O I：
10.3233/ASY-2012-1098
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页码：273 / 301
页数：29
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