Critical exponent for semi-linear structurally damped wave equation of derivative type

被引：13

作者：

Tuan Anh Dao ^{[1
,2
]}

Fino, Ahmad Z. ^{[3
]}

机构：

[1] Hanoi Univ Sci & Technol, Sch Appl Math & Informat, Hanoi, Vietnam

[2] TU Bergakad Freiberg, Fac Math & Comp Sci, Freiberg, Germany

[3] Lebanese Univ, Fac Sci, Dept Math, POB 1352, Tripoli, Lebanon

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2020年 / 43卷 / 17期

关键词：

critical exponent; fractional Laplacian; nonlinear evolution equations; structural damping; EXISTENCE;

D O I：

10.1002/mma.6649

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main purpose of this paper is to study the following semi-linear structurally damped wave equation with nonlinearity of derivative type: u(tt) - Delta u + mu(-Delta)(sigma/2)u(t) = vertical bar u(t vertical bar)(p), u(0,x) = u(0)(x), u(t)(0,x) = u(1)(x), with mu > 0, n >= 1, sigma is an element of(0,2], and p > 1. In particular, we would like to prove the nonexistence of global weak solutions by using a new test function and suitable sign assumptions on the initial data in both the subcritical case and the critical case.

引用

页码：9766 / 9775

页数：10

共 19 条

[1] A NECESSARY AND SUFFICIENT CONDITIONS FOR EXISTENCE OF NON NEGATIVE SOLUTIONS FOR SOME SEMILINEAR NON MONOTONE EQUATIONS [J].