Theoretical study of nonlinear wave equations with combined power-type nonlinearities with variable coefficients
Analysis of PDEs
2023-10-31 v1
Abstract
In this paper, we study the initial boundary value problem for the nonlinear wave equation with combined power-type nonlinearities with variable coefficients. The global behavior of the solutions with non-positive and sub-critical energy is completely investigated. The threshold between the nonexistence of global in time weak solutions and non-blowing up solutions is found. For super-critical energy, two new sufficient conditions guaranteeing nonexistence of global in time solutions are given. One of them is proved for arbitrary sign of the scalar product of the initial data, while the other one is derived only for positive sign. Uniqueness and existence of local weak solutions are proved.
Cite
@article{arxiv.2310.18775,
title = {Theoretical study of nonlinear wave equations with combined power-type nonlinearities with variable coefficients},
author = {Milena Dimova and Natalia Kolkovska and Nikolai Kutev},
journal= {arXiv preprint arXiv:2310.18775},
year = {2023}
}
Comments
33 pages