Quasilinear Hyperbolic Equations. Exponential Dichotomy and Solvability in Spaces of Functions Bounded and Almost Periodic in Time

L. R. Volevich, A. R. Shirikyan


Abstract: The existence of global solutions to high-order quasilinear hyperbolic equations is studied. It is assumed that the equation in question is a small perturbation of an equation with constant coefficients whose characteristic polynomial does not vanish in an open strip containing the imaginary axis. Under these conditions the property of exponential dichotomy and solvability in spaces of functions uniformly bounded in time are established. It is also proved that if the coefficients and right-hand side of the equation are periodic (almost periodic) in time, then there is at least one periodic (almost periodic) solution.