Polynomial decay for a hyperbolic-parabolic coupled system ∗

@inproceedings{Rauch2004PolynomialDF,
  title={Polynomial decay for a hyperbolic-parabolic coupled system ∗},
  author={Jeffrey Rauch and Xu Zhang and Enrique Zuazua},
  year={2004}
}
This paper analyzes the long time behavior of a linearized model for fluid-structure interaction. The space domain consists of two parts in which the evolution is governed by the heat equation and the wave equation respectively, with transmission conditions at the interface. Based on the construction of ray-like solutions by means of Geometric Optics expansions and a careful analysis of the transfer of the energy at the interface, we show the lack of uniform decay of solutions in general… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-10 of 21 references

Gaussian beams and the propagation of singularities

  • J. Ralston
  • Studies in Partial Differential Equations, Edited…
  • 1982
Highly Influential
10 Excerpts

Controllability of parabolic and hyperbolic equations: towards a unified theory

  • W. Li, X. Zhang
  • 2003
1 Excerpt

Observability estimate for the ultra-parabolic equations, 2003, in submission

  • W. Li
  • 2003
1 Excerpt

Explicit observability estimate for the wave equation with potential and its application

  • X. Zhang
  • Royal Soc. Lond. Proc. Ser. A Math. Phys. Eng…
  • 2000
1 Excerpt

Refraction of high-frequency waves density by sharp interfaces and semiclassical measures at the boundary

  • L. Miller
  • J. Math. Pures Appl., 79
  • 2000
1 Excerpt

The cost of approximate controllability for heat equations: the linear case

  • E. Fernández-Cara, E. Zuazua
  • Adv. Differential Equations, 5
  • 2000
2 Excerpts

Stabilisation de l’équation des ondes par le bord

  • G. Lebeau, L. Robbiano
  • Duke Math. J., 86
  • 1997