具有界面的Korteweg-de Vries方程

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2025-09-17 DOI:10.1111/sapm.70117

Hsin-Yuan Huang, Cheng-Pu Lin

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引用次数: 0

摘要

本文考虑带界面实线上的Korteweg-de Vries （KdV）方程。利用Fokas的统一变换方法，导出了带界面的线性强迫KdV方程的显式解公式。在这些解公式的基础上，我们建立了适当Sobolev空间中线性解的标准估计和非线性项的双线性估计。利用这些估计和一个收缩映射论证，我们证明了具有界面的KdV方程的局部适定性。

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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The Korteweg-de Vries Equation With an Interface

In this paper, we consider the Korteweg–de Vries (KdV) equation on the real line with an interface. Using Fokas's unified transform method, the explicit solution formulas for the linear forced KdV equation with an interface are derived. Building on these solution formulas, we establish standard estimates for the linear solution and a bilinear estimate for the nonlinear term in a suitable Sobolev space. Using these estimates and a contraction mapping argument, we prove the local well-posedness for the KdV equation with an interface.

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来源期刊

Studies in Applied Mathematics 数学-应用数学

CiteScore

4.30

自引率

3.70%

发文量

审稿时长

>12 weeks

期刊介绍： Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.