Considering a system of equations modeling the chevron pattern dynamics, we show that the corresponding initial boundary value problem has a unique weak solution that continuously depends on initial data, and the semigroup generated by this problem in the phase space $X^0:= L^2(\Omega)\times L^2(\Omega)$ has a global attractor. We also provide some insight to the behavior of the system, by reducing it under special assumptions to systems of ODEs, that can in turn be studied as dynamical systems.

中文翻译：

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V 形模式方程解的全局行为

考虑对人字纹动力学建模的方程组，我们表明相应的初始边值问题具有唯一的弱解，该弱解持续依赖于初始数据，并且该问题在相空间 $X^0:= L 中生成的半群^2(\Omega)\times L^2(\Omega)$ 具有全局吸引子。我们还提供了对系统行为的一些见解，通过在特殊假设下将其简化为 ODE 系统，进而可以作为动态系统进行研究。