$$H^1$$ solutions for a Kuramoto–Sinelshchikov–Cahn–Hilliard type equation
$$H^1$$ 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, the spatiotemporal evolution of the morphology of steps on crystal surfaces and the growth of thermodynamically unstable crystal surfaces with strongly anisotropic surface tension. In this paper, we prove the well-posedness of the Cauchy …