The Blow-Up of Solutions for a Class of Semi-linear Equations with p-Laplacian Viscoelastic Term Under Positive Initial Energy

被引：1

作者：

Wu, Xiulan ^{[1
]}

Yang, Xiaoxin ^{[1
]}

Zhao, Yaxin ^{[1
]}

机构：

[1] Changchun Univ Sci & Technol, Sch Math & Stat, Changchun 130022, Peoples R China

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2023年 / 20卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Semi-linear equations; p-Laplacian; viscoelastic term; blow up; positive initial energy; HEAT-EQUATION;

D O I：

10.1007/s00009-023-02440-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with homogeneous Dirichlet boundary value problem to a class of semi-linear equations with p-Laplacian viscoelastic term?u/?t - ?u + ?(t)(0)g(t - s)?(p)u(x, s)ds = |u|(q(x)-2) u, x ? O, t = 0, 0 the bounded domain O C R-n (n = 3) with a smooth boundary. We prove that the weak solutions of the above problems blow up in finite time for all 2k < q(-) < q(+) < p < 2n/n-2 (k is defined in (2.5)), when the initial energy is positive and the function g satisfies suitable conditions. This result generalized and improved the result by Messaoudi (Abstr Appl Anal 2005(2):87-94, 2005).

引用

页数：18

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