The interplay of critical regularity of nonlinearities in a weakly coupled system of semi-linear damped wave equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:299

Article

Tuan Anh Dao^1,2  Reissig, Michael³ 

[1] Hanoi Univ Sci & Technol, Sch Appl Math & Informat, 1 Dai Co Viet Rd, Hanoi, Vietnam

[2] Vietnam Acad Sci & Technol, Inst Math, 18 Hoang Quoc Viet Rd, Hanoi, Vietnam

[3] TU Bergakad Freiberg, Fac Math & Comp Sci, Pruferstr 9, D-09596 Freiberg, Germany

关键词: Damped wave equations;    Weakly coupled system;    Modulus of continuity;    Global existence;    Blow-up;   

DOI  :  10.1016/j.jde.2021.06.039

来源: Elsevier

【 摘 要 】

We would like to study a weakly coupled system of semi-linear classical damped wave equations with moduli of continuity in nonlinearities whose powers belong to the critical curve in the p - q plane. The main goal of this paper is to find out sharp conditions of these moduli of continuity which classify between global (in time) existence of small data solutions and finite time blow-up of (even) small data solutions. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free