一类两折鞍点抛物微分方程的存在性结果

Pub Date : 2024-01-09 DOI:10.1007/s10986-023-09616-w

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引用次数: 0

摘要

摘要我们提出并分析了一个抽象框架，用于研究线性退化抛物线增强混合方程组的良好求解性。我们将线性退化抛物线问题的理论与有关静态二重鞍点方程的结果相结合，推导出该问题解的存在性和唯一性的充分条件。最后，我们通过流体动力学和电磁问题的实例展示了所开发理论的一些应用。

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Existence results for a class of two-fold saddle point parabolic differential equations

Abstract

We propose and analyze an abstract framework to study the well-posedness for a family of linear degenerate parabolic augmentedmixed equations.We combine the theory for linear degenerate parabolic problems with results about stationary two-fold saddle point equations to deduce sufficient conditions for the existence and uniqueness of a solution for the problem. Finally, we show some applications of the developed theory through examples that come from fluid dynamic and electromagnetic problems.

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