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

[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.

[学科分类] 航空航天科学

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