General stability and exponential growth of nonlinear variable
coefficient wave equation with logarithmic source and memory term
- Long Yan
, - Lili Sun
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. This model describes wave travelling
through nonhomogeneous viscoelastic materials. By choosing appropriate
multiplier and using weighted energy method, we prove the exponential
decay of the energy. Besides, we also obtain the instability at the
infinity of the solutions in the presence of the nonlinear damping.03 Aug 2021Submitted to Mathematical Methods in the Applied Sciences 04 Aug 2021Submission Checks Completed
04 Aug 2021Assigned to Editor
24 Aug 2021Reviewer(s) Assigned
17 Nov 2021Review(s) Completed, Editorial Evaluation Pending
23 Nov 2021Editorial Decision: Revise Major
28 Jan 20221st Revision Received
28 Jan 2022Submission Checks Completed
28 Jan 2022Assigned to Editor
28 Jan 2022Reviewer(s) Assigned
29 Jan 2022Review(s) Completed, Editorial Evaluation Pending
02 Feb 2022Editorial Decision: Revise Minor
03 Feb 20222nd Revision Received
04 Feb 2022Submission Checks Completed
04 Feb 2022Assigned to Editor
15 Mar 2022Reviewer(s) Assigned
21 Jun 2022Review(s) Completed, Editorial Evaluation Pending
24 Jun 2022Editorial Decision: Accept
15 Jan 2023Published in Mathematical Methods in the Applied Sciences volume 46 issue 1 on pages 879-894. 10.1002/mma.8554 
