Abstract

We study the Cauchy problem for nonlinear degenerate parabolic equations with almost periodic initial data. Existence and uniqueness (in the Besicovitch space) of entropy solutions are established. It is demonstrated that the entropy solution remains to be spatially almost periodic and that its spectrum (more precisely, the additive group generated by the spectrum) does not increase in the time variable. Under a precise nonlinearity-diffusivity condition on the input data we establish the long time decay property in the Besicovitch norm. For the proof we use reduction to the periodic case and ergodic methods.

中文翻译：

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近周期初始数据非线性退化抛物方程熵解的衰减

摘要

我们研究了具有几乎周期性初始数据的非线性退化抛物线方程的柯西问题。熵解的存在性和唯一性（在 Besicovitch 空间中）被建立。证明熵解在空间上几乎是周期性的，并且它的光谱（更准确地说，由光谱产生的加性群）在时间变量中没有增加。在输入数据的精确非线性扩散条件下，我们在 Besicovitch 范数中建立了长时间衰减特性。为了证明，我们使用归约到周期案例和遍历方法。