Blow up of solutions for viscoelastic wave equations of Kirchhoff type with arbitrary positive initial energy
Date
2017-10-04
Authors
Piskin, Erhan
Fidan, Ayse
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article we consider the nonlinear Viscoelastic wave equations of Kirchhoff type
utt - M(∥∇u∥2) ∆u + ∫t0 g1(t - τ)∆u(τ)dτ + ut = (p + 1)|v|q+1|u|p-1u,
vtt - M(∥∇v∥2)∆v + ∫t0 g2(t - τ)∆v(τ)dτ + vτ = (q + 1)|u|p+1|v|q-1v
with initial conditions and Dirichlet boundary conditions. We proved the global nonexistence of solutions by applying a lemma by Levine, and the concavity method.
Description
Keywords
Blow up, Viscoelastic wave equation, Arbitrary positive initial energy
Citation
Piskin, E., & Fidan, A. (2017). Blow up of solutions for viscoelastic wave equations of Kirchhoff type with arbitrary positive initial energy. <i>Electronic Journal of Differential Equations, 2017</i>(242), pp. 1-10.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.