Modified different nonlinearities for weakly coupled systems of semilinear effectively damped waves with different time-dependent coefficients in the dissipation terms

Advances in Difference Equations

article

Mohammed Djaouti, Abdelhamid¹ 

[1] King Faisal University

关键词: Weakly coupled hyperbolic systems;    Damped wave equations;    Cauchy problem;    Global existence;    \(L^{2}\) -decay;    Effective dissipation;    Small data solutions;   

DOI  :  10.1186/s13662-021-03215-0

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

We prove the global existence of small data solution in all spaces of all dimensions$n\geq 1$ for weakly coupled systems of semilinear effectively damped wave, with different time-dependent coefficients in the dissipation terms. Moreover, we assume that the nonlinearity terms$f(t,u) $ and$g(t,v) $ satisfy some properties of parabolic equations. We study the problem in several classes of regularity.

【 授权许可】

CC BY