Nonexistence of global solutions to Klein-Gordon equations with variable coefficients power-type nonlinearities-Reference-Cited by-同舟云学术

Nonexistence of global solutions to Klein-Gordon equations with variable coefficients power-type nonlinearities

Published:2023-01-01 Issue:1 Volume:21 Page:
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Kolkovska Natalia¹,Dimova Milena²,Kutev Nikolai¹

Affiliation:

1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, G. Bonchev st, bl.8 , 1113 Sofia , Bulgaria

2. Faculty of Applied Informatics and Statistics, University of National and World Economy, 1700 , Sofia , Bulgaria

Abstract

Abstract In this article, we investigate the Cauchy problem for Klein-Gordon equations with combined power-type nonlinearities. Coefficients in the nonlinearities depend on the space variable. They are sign preserving functions except one of the coefficients, which may change its sign. We study completely the structure of the Nehari manifold. By using the potential well method, we give necessary and sufficient conditions for nonexistence of global solution for subcritical initial energy by means of the sign of the Nehari functional. When the energy is positive, we propose new sufficient conditions for finite time blow up of the weak solutions. One of these conditions is independent of the sign of the scalar product of the initial data. We also prove uniqueness of the weak solutions under slightly more restrictive assumptions for the powers of the nonlinearities.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2022-0584/pdf

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