Blowup and asymptotic stability of weak solutions to wave equations with nonlinear degenerate damping and source terms

Date

2007-05-22

Authors

Hu, Qingying
Zhang, Hongwei

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University-San Marcos, Department of Mathematics

Abstract

This article concerns the blow-up and asymptotic stability of weak solutions to the wave equation utt - Δu + |u|kj′(ut) = |u|p-1</sup>u in Ω x (0, T), where p > 1 and j′ denotes the derivative of a C1 convex and real value function j. We prove that every weak solution is asymptotically stability, for every m is such that 0 < m < 1, p < k + m and the initial energy is small; the solutions blow up in finite time, whenever p > k + m and the initial data is positive, but appropriately bounded.

Description

Keywords

Wave equation, Degenerate damping and source terms, Asymptotic stability, Blow up of solutions

Citation

Hu, Q., & Zhang, H. (2007). Blowup and asymptotic stability of weak solutions to wave equations with nonlinear degenerate damping and source terms. <i>Electronic Journal of Differential Equations, 2007</i>(76), pp. 1-10.

Rights

Attribution 4.0 International

Rights Holder

This work is licensed under a Creative Commons Attribution 4.0 International License.

Rights License