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

被引：10
|
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.
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页码：9766 / 9775
页数：10
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