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April  1997, 3(2): 265-288. doi: 10.3934/dcds.1997.3.265

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, United States

Received  October 1995 Revised  May 1996 Published  January 1997

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.
Citation: George Avalos. Concerning the well-posedness of a nonlinearly coupled semilinear wave and beam--like equation. Discrete & Continuous Dynamical Systems, 1997, 3 (2) : 265-288. doi: 10.3934/dcds.1997.3.265
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