Existence and exponential decay of solutions for magnetic effected piezoelectric beams with second sound and distributed delay term. (English) Zbl 1536.35315
Summary: This paper is concerned with a system of magnetic effected piezoelectric beams with distributed delay term, where the heat flux is given by Cattaneo’s law (second sound). We prove the existence and the uniqueness of the solution using the semigroup theory. Then, we establish the exponential stability of the solution by introducing a suitable Lyapunov functional.
MSC:
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 35Q79 | PDEs in connection with classical thermodynamics and heat transfer |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 78A25 | Electromagnetic theory (general) |
| 80A10 | Classical and relativistic thermodynamics |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 93D15 | Stabilization of systems by feedback |
| 93D20 | Asymptotic stability in control theory |
| 35R07 | PDEs on time scales |
| 35B35 | Stability in context of PDEs |
| 74F05 | Thermal effects in solid mechanics |
| 74F15 | Electromagnetic effects in solid mechanics |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
Keywords:
piezoelectric beams; magnetic effect; distributed delay; second sound; wellposedness; exponential stabilityReferences:
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