Interface stabilization of a parabolic-hyperbolic pde system with delay in the interaction

Gilbert Peralta; Karl Kunisch

doi:10.3934/dcds.2018133

Article Contents

2018, Volume 38, Issue 6: 3055-3083. Doi: 10.3934/dcds.2018133

This issue Previous Article A singular cahn-hilliard-oono phase-field system with hereditary memory Next Article Liouville theorems for periodic two-component shallow water systems

Interface stabilization of a parabolic-hyperbolic pde system with delay in the interaction

Gilbert Peralta^1, , and
Karl Kunisch^2,3,

1.
Department of Mathematics and Computer Science, University of the Philippines Baguio, Governor Pack Road, 2600 Baguio, Philippines
2.
Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria
3.
RICAM Institute, Austrian Academy of Sciences, Altenbergerstrasse 69, 4040 Linz, Austria

* Corresponding author
* Corresponding author

Received: October 2017

Revised: January 2018

Published: June 2018

This work was supported in part by the ERC advanced grant 668998 (OCLOC) under the EUs H2020 research program.

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Abstract

A coupled parabolic-hyperbolic system of partial differential equations modeling the interaction of a structure submerged in a fluid is studied. The system being considered incorporates delays in the interaction on the interface between the fluid and the solid. We study the stability properties of the interaction model under suitable assumptions between the competing strengths of the delays and the feedback controls.

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Mathematics Subject Classification: Primary: 35M33, 93D20, 93D15.

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