Global behavior of the solutions to nonlinear wave equations with combined power-type nonlinearities with variable coefficients

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-09 DOI:10.1016/j.na.2024.113504

M. Dimova , N. Kolkovska , N. Kutev

引用次数: 0

Abstract

In this paper we study the initial boundary value problem for the nonlinear wave equation with combined power-type nonlinearities with variable coefficients. Existence and uniqueness of local weak solutions are proved. The global behavior of the solutions with non-positive and sub-critical energy is completely investigated. The threshold between global existence and finite time blow up is found. For super-critical energy, two new sufficient conditions guaranteeing blow up of the solutions for a finite time, are given. One of them is proved for an arbitrary sign of the scalar product of the initial data, while the other one is derived only for a positive sign.

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具有可变系数的组合功率型非线性非线性波方程解的全局行为

本文研究了具有可变系数的组合动力型非线性非线性波方程的初始边界值问题。证明了局部弱解的存在性和唯一性。完全研究了具有非正值和亚临界能量的解的全局行为。找到了全局存在与有限时间炸毁之间的临界点。对于超临界能量，给出了保证解在有限时间内炸毁的两个新的充分条件。其中一个是针对初始数据标量乘的任意符号证明的，而另一个仅针对正符号。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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