带空间非局部算子的超扩散方程温和解的良好拟合

IF 1.9 3区数学 Q1 MATHEMATICS

Qualitative Theory of Dynamical Systems Pub Date : 2024-07-02 DOI:10.1007/s12346-024-01084-y

Xuan-Xuan Xi, Yong Zhou, Mimi Hou

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引用次数: 0

摘要

本文研究了一类带有空间非局部算子的半线性超扩散方程的好拟性。我们首先建立了贝塞尔势空间中的 Gagliardo-Nirenberg 不等式。在此基础上，通过先验估计得到了相应线性问题的局部和全局温和解的拟合结果。我们还得到了非线性问题在不同条件下的良好求解结果。这些结论主要基于 Mihlin-Hörmander 乘数估计、嵌入定理和定点理论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Well-Posedness of Mild Solutions for Superdiffusion Equations with Spatial Nonlocal Operators

In this paper, we study the well-posedness for a class of semilinear superdiffusion equations with spatial nonlocal operators. We first establish the Gagliardo–Nirenberg inequality in \(\psi \)-Bessel potential spaces. Based on this, the well-posedness results of local and global mild solution for corresponding linear problem are obtained via apriori estimates. We also obtain the well-posedness results for the nonlinear problem under different conditions. These conclusions are mainly based on the Mihlin–Hörmander’s multiplier estimates, embedding theorem and fixed point theory.

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来源期刊

Qualitative Theory of Dynamical Systems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

14.30%

发文量

130

期刊介绍： Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.