Abstract
In this paper we consider the Cauchy problem for a higher-order viscoelastic wave equation with finite memory and nonlinear logarithmic source term. Under certain conditions on the initial data with negative initial energy and with certain class of relaxation functions, we prove a finite-time blow-up result in the whole space. Moreover, the blow-up time is estimated explicitly. The upper bound and the lower bound for the blow up time are estimated.
| Original language | English |
|---|---|
| Pages (from-to) | 1221-1232 |
| Number of pages | 12 |
| Journal | Discrete and Continuous Dynamical Systems - Series S |
| Volume | 15 |
| Issue number | 5 |
| DOIs | |
| State | Published - May 2022 |
Bibliographical note
Publisher Copyright:© 2022 American Institute of Mathematical Sciences. All rights reserved.
Keywords
- Blow up
- Cauchy problem
- lower bound
- memory
- nonlinear higher-order wave equation
- upper bound
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics