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

Abstract

Abstract We prove the global existence of small data solution in all spaces of all dimensions n ≥ 1 $n\geq 1$ 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 ) $f(t,u) $ and g ( t , v ) $g(t,v) $ satisfy some properties of parabolic equations. We study the problem in several classes of regularity.

Keywords

• Weakly coupled hyperbolic systems
• Damped wave equations
• Cauchy problem
• Global existence
• L 2 $L^{2}$ -decay
• Effective dissipation