Global Existence and Blow-up of Solutions for a System of Fractional Wave Equations

被引：4

作者：

Ahmad, Bashir ^{[1
]}

Alsaedi, Ahmed ^{[1
]}

Berbiche, Mohamed ^{[2
]}

Kirane, Mokhtar ^{[1
,3
]}

机构：

[1] King Abdulaziz Univ, Fac Sci, Dept Math, Nonlinear Anal & Appl Math NAAM Res Grp, POB 80203, Jeddah 21589, Saudi Arabia

[2] Biskra Univ, Lab Math Anal Probabil & Optimizat, BP 145, Biskra 07000, Algeria

[3] Khalifa Univ Sci & Technol, Coll Art & Sci, Dept Math, Abu Dhabi, U Arab Emirates

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2022年 / 26卷 / 01期

关键词：

coupled fractional-wave equations; polynomial nonlinearities; global solution; blow-up; CRITICAL EXPONENTS; FUJITA-TYPE; DIFFUSION; NONEXISTENCE; BEHAVIOR;

D O I：

10.11650/tjm/210804

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the Cauchy problem for a 2 x 2-system of weakly coupled semi-linear fractional wave equations with polynomial nonlinearities posed in R(+)xR(N). Under appropriate conditions on the exponents and the fractional orders of the time derivatives, it is shown that there exists a threshold value of the dimension N, for which, small data-global solutions as well as finite time blowing-up solutions exist. Furthermore, we investigate the L-infinity-decay estimates of global solutions.

引用

页码：103 / 135

页数：33

共 34 条

[1] Critical exponents of fujita type for inhomogeneous parabolic equations and systems [J].