Calculus of Variations and Geometric Measure Theory
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D. D. Monticelli - F. Punzo - M. Squassina

Nonexistence for hyperbolic problems on riemannian manifolds

created by squassina on 19 Jul 2018

[BibTeX]

Submitted Paper

Inserted: 19 jul 2018
Last Updated: 19 jul 2018

Year: 2018

Abstract:

We establish necessary conditions for the existence of solutions to a class of semilinear hyperbolic problems defined 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: Nonexistence of solutions, hyperbolic problems, wave equation


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