标题： 二维抛物系统中周期波的非线性稳定性 显示英文标题

标题： Nonlinear stability of two-dimensional periodic waves in parabolic systems with conservation laws

摘要： 我们为一般抛物型系统的二维周期行波发展了一种稳定性理论，可能包括守恒定律。 特别是，我们确定了一个扩散谱稳定性假设，并证明它对于各种（非）局部扰动，包括临界非局部扰动，意味着非线性稳定性。 因此，我们将Johnson等人的工作（Invent. Math. 2014）中的稳定性部分扩展到二维模式，并将Melinand-Rodrigues的预印本（2024）中的结果扩展到包含守恒定律的系统。 在此过程中，我们需要绕过两种低谱正则性，即由于多维性引起的显式锥形奇异性和由于守恒定律引起的约当块类似奇异性的干扰。 显示英文摘要

摘要： We develop a stability theory for two-dimensional periodic traveling waves of general parabolic systems, possibly including conservation laws. In particular, we identify a diffusive spectral stability assumption and prove that it implies nonlinear stability for variously-(non)localized perturbations, including critically nonlocalized perturbations. Thus we extend the stability parts of Johnson et al., Invent. Math. 2014, to two-dimensional patterns and of Melinand-Rodrigues, preprint 2024, to systems with conservation laws. In doing so we need to bypass two kinds of low spectral regularity, explicitly conic-like singularities due to multidimensionality and Jordan-block like singularities due to conservation laws.