Nonexistence for hyperbolic problems on Riemannian manifolds

Dario D. Monticelli; Fabio Punzo; Marco Squassina

doi:10.3233/ASY-191580

Nonexistence for hyperbolic problems on Riemannian manifolds

Dario D. Monticelli, Fabio Punzo, Marco Squassina

Polytechnic University of Milan

Risultato della ricerca: Contributo in rivista › Articolo in rivista

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.

Lingua originale	English
pagine (da-a)	1-15
Numero di pagine	15
Rivista	Asymptotic Analysis
DOI	https://doi.org/10.3233/ASY-191580
Stato di pubblicazione	Pubblicato - 2020

Keywords

Nonexistence results, hyperbolic problems

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10.3233/ASY-191580

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title = "Nonexistence for hyperbolic problems on Riemannian manifolds",

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 results, hyperbolic problems, Nonexistence results, hyperbolic problems",

author = "Monticelli, {Dario D.} and Fabio Punzo and Marco Squassina",

year = "2020",

doi = "10.3233/ASY-191580",

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journal = "Asymptotic Analysis",

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T1 - Nonexistence for hyperbolic problems on Riemannian manifolds

AU - Monticelli, Dario D.

AU - Punzo, Fabio

AU - Squassina, Marco

PY - 2020

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N2 - 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.

AB - 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.

KW - Nonexistence results, hyperbolic problems

UR - http://hdl.handle.net/10807/154902

U2 - 10.3233/ASY-191580

DO - 10.3233/ASY-191580

M3 - Article

SN - 0921-7134

SP - 1

EP - 15

JO - Asymptotic Analysis

JF - Asymptotic Analysis

ER -

Nonexistence for hyperbolic problems on Riemannian manifolds

Abstract

Keywords

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