Open AccessInstantaneous blow-up for nonlinear Sobolev type equations with potentials on Riemannian manifolds
Author(s) -
Mohamed Jleli,
Bessem Samet
Publication year - 2022
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2022036
Subject(s) - sobolev space , nonlinear system , mathematics , infinity , type (biology) , mathematical analysis , manifold (fluid mechanics) , riemannian manifold , polynomial , cauchy distribution , pure mathematics , physics , mechanical engineering , ecology , quantum mechanics , engineering , biology
We investigate Cauchy problems for two classes of nonlinear Sobolev type equations with potentials defined on complete noncompact Riemannian manifolds. The first one involves a polynomial nonlinearity and the second one involves a gradient nonlinearity. Namely, we derive sufficient conditions depending on the geometry of the manifold, the power nonlinearity, the behavior of the potential at infinity, and the initial data, for which the considered problems admit no nontrivial local weak solutions, i.e., an instantaneous blow-up occurs.