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About nonlinear electromagnetoelastic problemM. Vishnevskii & V. PriimenkoThere is considered the first initial boundary-value problem related to the electrodynamics of vibrating elastic media. The model under study consists of three coupled differential equations, one of them is a hyperbolic equation (an analog of the Lamé equations) and two other ones form a parabolic system (an analog of the diffusion Maxwell system). Existence and uniqueness results for a model describing the nonlinear interactions of the electromagnetic and elastic waves are established.
A converse lyapunov theorem for retarded functional differential equationsM. Federson, S. SchwabikWe consider retarded functional differential equations and state a converse Lyapunov-type theorem for these equations by means of the theory of generalized ODEs introduced by J. Kurzweil.