Algorithms, Vol. 13, Pages 77: On Classical Solutions for A Kuramoto--Sinelshchikov--Velarde-Type Equation (Algorithms)

The Kuramoto–Sinelshchikov–Velarde equation describes the evolution of a phase turbulence in reaction-diffusion systems or the evolution of the plane flame propagation, taking into 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 Cauchy problem.