Well-posedness and exponential stability of Timoshenko system of second sound with time-varying delay and forcing terms. (English) Zbl 1541.35060
Summary: As a continuity to the study by D. Ouchenane [Georgian Math. J. 21, No. 4, 475–489 (2014; Zbl 1304.35103)]. We consider a nonlinear thermoelastic system of Timoshenko type with a time-varing delay and forcing term. We show the well-posedness of the system by using the semigroup theory, and we prove an exponential stability result under the usual assumption on the wave speed by the energy method.
MSC:
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35G61 | Initial-boundary value problems for systems of nonlinear higher-order PDEs |
| 35L55 | Higher-order hyperbolic systems |
| 74D05 | Linear constitutive equations for materials with memory |
| 93D15 | Stabilization of systems by feedback |
| 93D20 | Asymptotic stability in control theory |
Keywords:
exponential decay; linear damping; Timoshenko; thermoelasticity; second sound; parabolic-hyperbolic systemCitations:
Zbl 1304.35103References:
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