What is it about?
This model describes the evolution of a system of two elastic membranes. The interaction of the membranes is given by the linear 0-th order term, where the parameter alpha positive is related with the properties of the system.
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Why is it important?
Stabilization of coupled systems of evolution equations was already considered. However, there the authors considered linear dampings, and the problem of (both internal and boundary) indirect stabilization. For such a system, the authors prove a polynomial decay of the total energy of the system, in contrast with the exponential rate for one single damped wave equation. In the paper under consideration, we generalizes the previous result to the case of non-linear dampings acting in both the equations, under suitable hypothesis on the non-linearities.
Perspectives
The hypotheses (both the equation are stabilized, the supports of the dampings are the same set, which is of non-zero measure) . We wonder if one could prove the same result under more general assumptions.
wenden charles
Federal University of Acre
Read the Original
This page is a summary of: A Stabilization for a Coupled Wave System with Nonlinear and Arbitrary Damping, Journal of Advances in Mathematics and Computer Science, February 2018, Sciencedomain International,
DOI: 10.9734/jamcs/2018/38196.
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