$$H^1$$ solutions for a Kuramoto–Sinelshchikov–Cahn–Hilliard type equation

Abstract The Kuramoto–Sinelshchikov–Cahn–Hilliard equation models the spinodal decomposition of phase separating systems in an external field, spatiotemporal evolution morphology steps on crystal surfaces and growth thermodynamically unstable with strongly anisotropic surface tension. In this paper, we prove well-posedness Cauchy problem, associated equation.