双分量福恩贝格-惠瑟姆系统弱解的存在和强解的膨胀

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Evolution Equations Pub Date : 2024-02-10 DOI:10.1007/s00028-023-00941-8

Zhihao Bai, Yang Wang, Long Wei

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引用次数: 0

摘要

在本文中，我们研究了双成分 Fornberg-Whitham 系统弱解的存在和强解的膨胀。由于缺乏一些有用的守恒定律，我们通过一种改进的伪抛物正则化方法，在低阶索波列夫空间 \(H^{s}\times H^{s-1}\) (\(s\in (1,3/2]\))中建立了该系统弱解的存在性。然后，展示了该系统强解的炸毁情形。通过最近对 Riccati-type 不等式的分析，我们提出了一些导致该系统相应强解炸毁的初始数据的充分条件。

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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Existence of a weak solution and blow-up of strong solutions for a two-component Fornberg–Whitham system

In this paper, we investigate the existence of a weak solution and blow-up of strong solutions to a two-component Fornberg–Whitham system. Due to the absence of some useful conservation laws, we establish the existence of a weak solution to the system in lower order Sobolev spaces \(H^{s}\times H^{s-1}\) (\(s\in (1,3/2]\)) via a modified pseudo-parabolic regularization method. And then, a blow-up scenario for strong solutions to this system is shown. By the analysis of Riccati-type inequalities recently, we present some sufficient conditions on the initial data that lead to the blow-up for corresponding strong solutions to the system.

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来源期刊

Journal of Evolution Equations 数学-数学

CiteScore

2.30

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Evolution Equations (JEE) publishes high-quality, peer-reviewed papers on equations dealing with time dependent systems and ranging from abstract theory to concrete applications. Research articles should contain new and important results. Survey articles on recent developments are also considered as important contributions to the field. Particular topics covered by the journal are: Linear and Nonlinear Semigroups Parabolic and Hyperbolic Partial Differential Equations Reaction Diffusion Equations Deterministic and Stochastic Control Systems Transport and Population Equations Volterra Equations Delay Equations Stochastic Processes and Dirichlet Forms Maximal Regularity and Functional Calculi Asymptotics and Qualitative Theory of Linear and Nonlinear Evolution Equations Evolution Equations in Mathematical Physics Elliptic Operators