Well-posedness result for the Kuramoto-Velarde equation

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

Automated summary

The Kuramoto-Velarde equation describes slow space-time variations of disturbances at interfaces and plasma instability fronts. It also proves the well-posedness of classical solutions for the Cauchy problem under appropriate assumptions on initial data, time, and coefficients.