# Decay Rates of Interactive Hyperbolic-Parabolic PDE Models with Thermal Effects on the Interface

Decay Rates of Interactive Hyperbolic-Parabolic PDE Models with Thermal Effects on the Interface We consider coupled PDE systems comprising of a hyperbolic and a parabolic-like equation with an interface on a portion of the boundary. These models are motivated by structural acoustic problems. A specific prototype consists of a wave equation defined on a three-dimensional bounded domain Ω coupled with a thermoelastic plate equation defined on Γ 0—a flat surface of the boundary \partial Ω . Thus, the coupling between the wave and the plate takes place on the interface Γ 0. The main issue studied here is that of uniform stability of the overall interactive model. Since the original (uncontrolled) model is only strongly stable, but not uniformly stable, the question becomes: what is the minimal amount'' of dissipation necessary to obtain uniform decay rates for the energy of the overall system? http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# Decay Rates of Interactive Hyperbolic-Parabolic PDE Models with Thermal Effects on the Interface

, Volume 42 (2) – Jan 1, 2000
41 pages

/lp/springer_journal/decay-rates-of-interactive-hyperbolic-parabolic-pde-models-with-KuVRwvaLpt
Publisher
Springer-Verlag
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s002450010010
Publisher site
See Article on Publisher Site

### Abstract

We consider coupled PDE systems comprising of a hyperbolic and a parabolic-like equation with an interface on a portion of the boundary. These models are motivated by structural acoustic problems. A specific prototype consists of a wave equation defined on a three-dimensional bounded domain Ω coupled with a thermoelastic plate equation defined on Γ 0—a flat surface of the boundary \partial Ω . Thus, the coupling between the wave and the plate takes place on the interface Γ 0. The main issue studied here is that of uniform stability of the overall interactive model. Since the original (uncontrolled) model is only strongly stable, but not uniformly stable, the question becomes: what is the minimal amount'' of dissipation necessary to obtain uniform decay rates for the energy of the overall system?

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jan 1, 2000

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