关于带阻尼项的广义布森斯克方程的考希问题

IF 1.2 4区数学 Q1 MATHEMATICS

Acta Mathematica Scientia Pub Date : 2024-08-27 DOI:10.1007/s10473-024-0508-1

Xiao Su, Shubin Wang

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引用次数: 0

摘要

本文主要研究自然能量空间中带有非线性源项的广义阻尼布森斯克方程的考希问题。借助线性时空估计，我们利用收缩映射原理建立了解的局部存在性和唯一性。在亚临界和临界初始能量水平上，我们得到了解的全局存在性和炸毁性。此外，我们还构建了任意正初始能量下解的有限时间炸毁的充分条件。

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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On the Cauchy problem for the generalized Boussinesq equation with a damped term

This paper is devoted to the Cauchy problem for the generalized damped Boussinesq equation with a nonlinear source term in the natural energy space. With the help of linear time-space estimates, we establish the local existence and uniqueness of solutions by means of the contraction mapping principle. The global existence and blow-up of the solutions at both subcritical and critical initial energy levels are obtained. Moreover, we construct the sufficient conditions of finite time blow-up of the solutions with arbitrary positive initial energy.

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来源期刊

Acta Mathematica Scientia 数学-数学

CiteScore

2.00

自引率

10.00%

发文量

2614

审稿时长

6 months

期刊介绍： Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981. The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.