publication . Preprint . 2014

A note on optimal regularity and regularizing effects of point mass coupling for a heat-wave system

Muha, Boris;
Open Access English
  • Published: 16 Mar 2014
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.
free text keywords: Mathematics - Analysis of PDEs, 35M33, 35B65, 74F10, 35Q35
Funded by
NSF| Fluid-multi-layered-structure interaction problems
  • Funder: National Science Foundation (NSF)
  • Project Code: 1311709
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
MZOS| Mathematical analysis of composite and thin structures
  • Funder: Ministry of Science, Education and Sports of the Republic of Croatia (MSES) (MZOS)
  • Project Code: 037-0693014-2765
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