On a Kuramoto-Velarde type equation

Abstract

Kuramoto-Velarde-type equations describe the evolution of the spinodal decomposition of phase-separating systems in an external field, or, the spatiotemporal evolution of the morphology of steps on crystal surfaces. Under appropriate assumptions on the initial data, on the time T, and on the coefficients of such equation, we prove the well-posedness of the classical solutions for the Cauchy problem, associated with this equation.