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General stability and exponential growth of nonlinear variable coefficient wave equation with logarithmic source and memory term.
- Source :
-
Mathematical Methods in the Applied Sciences . Jan2023, Vol. 46 Issue 1, p879-894. 16p. - Publication Year :
- 2023
-
Abstract
- This paper is concerned with the asymptotic stability and instability of solutions to a variable coefficient logarithmic wave equation with nonlinear damping and memory term. Such model describes wave traveling through nonhomogeneous viscoelastic materials. By choosing appropriate multiplier and using weighted energy method, we prove the exponential decay of the energy. Moreover, we also obtain the instability of the solutions at the infinity in the presence of the nonlinear damping. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01704214
- Volume :
- 46
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Mathematical Methods in the Applied Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 160812551
- Full Text :
- https://doi.org/10.1002/mma.8554