A Positivity Criterion for the Wave Equation and Global Existence of Large Solutions-Reference-Cited by-同舟云学术

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A Positivity Criterion for the Wave Equation and Global Existence of Large Solutions

Published:2023-06-20 Issue:20 Volume:2023 Page:17911-17952
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Beceanu Marius¹,Soffer Avy²

Affiliation:

1. Department of Mathematics and Statistics , University at Albany SUNY, Earth Science 110, Albany, NY 12222, USA

2. Department of Mathematics , Rutgers University, 110 Frelinghuysen Rd, Piscataway, NJ 08854, USA

Abstract

Abstract In dimensions one to three, the fundamental solution to the free wave equation is positive. Therefore, there exists a simple positivity criterion for solutions. We use this to obtain large global solutions to two well-studied energy-supercritical semilinear wave equations, as well as some new results in the subcritical and critical cases.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/article-pdf/2023/20/17911/52414646/rnad127.pdf

Reference51 articles.

1. A center-stable manifold for the energy-critical wave equation in ${\mathbb {R}}^3$in the symmetric setting;Beceanu;J. Hyper. Differential Equations,2014

2. Strichartz estimates and maximal operators for the wave equation in ${\mathbb {R}}^3$;Beceanu;J. Funct. Anal.,2014

3. Large outgoing solutions to supercritical wave equations;Beceanu

4. Large initial data global well-posedness for a supercritical wave equation;Beceanu

5. Superlinear indefinite elliptic problems and nonlinear Liouville theorems;Berestycki;Topoi. Methods Nonlinear Anal.,1993

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