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
Abstract
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.
Subjects
free text keywords: Mathematics - Analysis of PDEs, 35M33, 35B65, 74F10, 35Q35
Funded by
NSF| Fluid-multi-layered-structure interaction problems
Project
  • 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
Project
  • Funder: Ministry of Science, Education and Sports of the Republic of Croatia (MSES) (MZOS)
  • Project Code: 037-0693014-2765
Download from
26 references, page 1 of 2

[1] George Avalos, Irena Lasiecka, and Roberto Triggiani. Higher regularity of a coupled parabolic-hyperbolic uid-structure interactive system. Georgian Math. J., 15(3):403{437, 2008.

[3] Viorel Barbu, Zoran Grujic, Irena Lasiecka, and Amjad Tu aha. Smoothness of weak solutions to a nonlinear uid-structure interaction model. Indiana Univ. Math. J., 57(3):1173{1207, 2008.

[4] Ham Brezis. Analyse fonctionnelle. Collection Mathematiques Appliquees pour la Ma^trise. [Collection of Applied Mathematics for the Master's Degree]. Masson, Paris, 1983. Theorie et applications. [Theory and applications].

[5] M. Bukac, S. Canic, and B. Muha. A partitioned scheme for uid-composite structure interaction problems. submitted, 2013. [OpenAIRE]

[6] P. Causin, J. F. Gerbeau, and F. Nobile. Added-mass e ect in the design of partitioned algorithms for uid-structure problems. Comput. Methods Appl. Mech. Engrg., 194(42-44):4506{4527, 2005. [OpenAIRE]

[7] Daniel Coutand and Steve Shkoller. Motion of an elastic solid inside an incompressible viscous uid. Arch. Ration. Mech. Anal., 176(1):25{102, 2005.

[8] Daniel Coutand and Steve Shkoller. The interaction between quasilinear elastodynamics and the Navier-Stokes equations. Arch. Ration. Mech. Anal., 179(3):303{352, 2006.

[9] Q. Du, M. D. Gunzburger, L. S. Hou, and J. Lee. Analysis of a linear uidstructure interaction problem. Discrete Contin. Dyn. Syst., 9(3):633{650, 2003.

[10] Thomas Duyckaerts. Optimal decay rates of the energy of a hyperbolicparabolic system coupled by an interface. Asymptot. Anal., 51(1):17{45, 2007.

[11] Giovanni P. Galdi. On the motion of a rigid body in a viscous liquid: a mathematical analysis with applications. In Handbook of mathematical uid dynamics, Vol. I, pages 653{791. North-Holland, Amsterdam, 2002.

[12] Scott Hansen and Enrique Zuazua. Exact controllability and stabilization of a vibrating string with an interior point mass. SIAM J. Control Optim., 33(5):1357{1391, 1995.

[13] Mihaela Ignatova, Igor Kukavica, Irena Lasiecka, and Amjad Tu aha. On well-posedness for a free boundary uid-structure model. J. Math. Phys., 53(11):115624, 13, 2012.

[14] Herbert Koch and Enrique Zuazua. A hybrid system of PDE's arising in multi-structure interaction: coupling of wave equations in n and n 1 space dimensions. In Recent trends in partial di erential equations, volume 409 of Contemp. Math., pages 55{77. Amer. Math. Soc., Providence, RI, 2006.

[15] I. Kukavica and A. Tu aha. Solutions to a uid-structure interaction free boundary problem. DCDS-A, 32(4):1355{1389, 2012.

[16] Igor Kukavica and Amjad Tu aha. Solutions to a free boundary problem of uid-structure interaction. Indiana Univ. Math. J., 61:1817{1859, 2012.

26 references, page 1 of 2
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue