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On the initial-boundary value problem for a Kuramoto-Sinelshchikov type equation

1 Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, via E. Orabona 4, 70125 Bari, Italy
2 Dipartimento di Matematica, Universita di Bari, via E. Orabona 4, 70125 Bari, Italy

The Kuramoto-Sinelshchikov equation describes the evolution of a phase turbulence in reaction-diffusion systems or the evolution of the plane flame propagation, taking in account the combined influence of diffusion and thermal conduction of the gas on the stability of a plane flame front. In this paper, we prove the well-posedness of the classical solutions for the initial-boundary value problem for this equation, under appropriate boundary conditions.
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