Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 425, Issue 2, Pages 1134-1147Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2015.01.018
Keywords
Heat-wave system; Fluid-structure interaction; Hyperbolic-parabolic coupling; Coupling through point mass; Optimal regularity
Categories
Funding
- ESF OPT-PDE - Exchange Grant [4171]
- National Science Foundation [DMS-1311709]
- MZOS [0037-0693014-2765]
- Croatian Science Foundation [9477]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1311709] Funding Source: National Science Foundation
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We consider a coupled 1D heat-wave system which serves as a simplified fluid structure interaction problem. The system is coupled in two different ways: the first, when the interface does not have mass and the second, when the interface does have mass. We prove an optimal regularity result in Sobolev spaces for both cases. The main idea behind the proof is to reduce the coupled problem to a single nonlocal equation on the interface by using Neummann to Diriclet operator. Furthermore, we show that point mass coupling regularizes the problem and quantify this regularization in the sense of Sobolev spaces. (C) 2015 Elsevier Inc. All rights reserved.
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