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 problem, associated with this equation.

中文翻译：

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$$H^1$$ H 1 Kuramoto–Sinelshchikov–Cahn–Hilliard 型方程的解

Kuramoto-Sinelshchikov-Cahn-Hilliard 方程模拟了外场中相分离系统的旋节线分解、晶体表面台阶形态的时空演化以及具有强各向异性表面张力的热力学不稳定晶体表面的生长。在本文中，我们证明了与该方程相关的柯西问题的适定性。