Nonexistence for hyperbolic problems on Riemannian manifolds
Analysis of PDEs
2018-07-20 v1
Abstract
We establish necessary conditions for the existence of solutions to a class of semilinear hyperbolic problems on complete noncompact Riemannian manifolds, extending some nonexistence results for the wave operator with power nonlinearity on the whole Euclidean space. A general weight function depending on spacetime is allowed in front of the power nonlinearity.
Keywords
Cite
@article{arxiv.1807.07316,
title = {Nonexistence for hyperbolic problems on Riemannian manifolds},
author = {Dario D. Monticelli and Fabio Punzo and Marco Squassina},
journal= {arXiv preprint arXiv:1807.07316},
year = {2018}
}