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Thermoelastic stability of a composite material. (English) Zbl 1448.35036

Summary: We consider transmission problems for a coupling of a string and a beam with at least one of them being thermoelastic. The heat conduction is modeled by Fourier’s law. We prove that the associated semigroup is exponentially stable when the string is thermoelastic. If only the beam is thermoelastic the system is always polynomially stable, but non exponentially stable for a large class of beams.

MSC:

35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35G46 Initial-boundary value problems for systems of linear higher-order PDEs
74F05 Thermal effects in solid mechanics
93D20 Asymptotic stability in control theory
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