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

George Avalos

doi:10.3934/dcds.1997.3.265

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1997, Volume 3, Issue 2: 265-288. Doi: 10.3934/dcds.1997.3.265

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

George Avalos^1,

1.
Department of Mathematics, Texas Tech University, Lubbock, Texas 79409-1042

Received: September 30, 1995

Revised: April 30, 1996

Published: March 1997

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Abstract

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.

Keywords:

Hyperbolic/parabolic system,
semilinear wave and beam-like equation.

Mathematics Subject Classification: 35M10, 35D05, 35B37.

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