The Kuramto–Sivashinsky equation with anisotropy effects 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. Written in terms of the step slope, it can be represented in a form similar to a convective Cahn–Hilliard equation. In this paper, we prove the well-posedness of the classical solutions for the Cauchy problem, associated with this equation.

中文翻译：

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具有各向异性效应的Kuramto-Sivashinsky方程经典解的适定性

具有各向异性效应的Kuramto-Sivashinsky方程可模拟外部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。用阶跃斜率表示，可以用类似于对流Cahn-Hilliard方程的形式表示。在本文中，我们证明了与该方程有关的柯西问题经典解的适定性。