论文标题
一般领域中复杂的金兹堡 - 兰道方程的局部适应性
Local well-posedness of the complex Ginzburg-Landau Equation in general domains
论文作者
论文摘要
在本文中，研究了具有超线增长项的复杂的金茨堡 - 兰道（CGL）方程。我们讨论了能量空间H1中的局部良好性，以针对一般域中的方程的初始符号值问题。作者（2019年）已经检查了界面域中H1中的本地适合性。我们对CGL方程的方法基于由具有非偶然扰动的细分差异操作员控制的抛物线方程理论。通过将此方法与Yosida近似程序一起使用，我们讨论了局部解决方案的存在和独特性以及具有较小初始数据的解决方案的全球存在。
In this paper, complex Ginzburg-Landau (CGL) equations with superlinear growth terms are studied. We discuss the local well-posedness in the energy space H1 for the initial-boundary value problem of the equations in general domains. The local well-posedness in H1 in bounded domains is already examined by authors (2019). Our approach to CGL equations is based on the theory of parabolic equations governed by subdifferential operators with non-monotone perturbations. By using this method together with the Yosida approximation procedure, we discuss the existence and the uniqueness of local solutions as well as the global existence of solutions with small initial data.
