Direct problem for a nonlinear evolutionary system. (English) Zbl 1194.35491
Summary: We consider the first initial boundary-value problem for an evolutionary system describing nonlinear interactions of electromagnetic and elastic waves. The system under study consists of three coupled differential equations, one of them is a hyperbolic equation (an analogue of the Lamé equation) and the other two equations form a parabolic system (an analogue of the diffusion Maxwell system). Existence and uniqueness results are established. We also prove the stability estimate of a weak solution.
MSC:
| 35R15 | PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) |
| 78A40 | Waves and radiation in optics and electromagnetic theory |
| 74J99 | Waves in solid mechanics |
| 35D30 | Weak solutions to PDEs |
| 35B35 | Stability in context of PDEs |
| 74F15 | Electromagnetic effects in solid mechanics |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
nonlinear evolutionary system; Faedo-Galerkin method; uniqueness and existence theorems; stability resultReferences:
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