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Concerning the well-posedness of a nonlinearly coupled semilinear wave and beam--like equation

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  • In this work, we show the local existence and uniqueness of a coupled hyperbolic/parabolic system, where the coupling is partially accomplished through a strongly nonlinear term of polynomial growth. We show ultimately that the degree of the nonlinearity allowed depends upon the smoothness of a "piece" of the initial data and the geometry where the equations take place, and under a relatively mild imposition of smoothness, one can solve the system for nonlinearities of arbitrary polynomial bound.
    Mathematics Subject Classification: 35M10, 35D05, 35B37.


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