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On a local in time solvability of the Neumann problem of quasilinear hyperbolic parabolic coupled systems. (English) Zbl 0841.35003
The author prvoes a local (in time) existence theorem of classical solutions to some coupled systems of quasilinear hyperbolic equations and quasilinear parabolic equations with Neumann boundary conditions which are fully nonlinear. An iteration scheme, extending that used by Y. Shibata and M. Kikuchi [J. Differ. Equations 80, 154-197 (1989; Zbl 0689.35055)] for a hyperbolic system, leads to the solution by successive approximation through appropriate linearization and the study of hyperbolic-parabolic-elliptic systems. The equations of nonlinear thermoelasticity are a typical example.
Reviewer: R.Racke (Konstanz)

35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
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