Well-posedness result for the Kuramoto–Velarde equation

Abstract The Kuramoto–Velarde equation describes slow space-time variations of disturbances at interfaces, diffusion–reaction fronts and plasma instability fronts. It also Benard–Marangoni cells that occur when there is large surface tension on the interface in a microgravity environment. Under appropriate assumption initial data, time T , coefficients such equation, we prove well-posedness classical solutions for Cauchy problem, associated with this equation.