Mild solutions of hyperbolic systems with L1 + and L∞ + initial data

Abstract

Abstract The three sections of the paper contain the following results: 1) Theorems concerning local existence, uniqueness and nonnegativity of mild solutions for semilinear, strictly hyperbolic systems with initial values in L∞ +(R3). 2) Results about the global existence of mild solutions for two examples of such systems (one example is the Carleman model) in one dimension when the initial data are in L1 Loc, +(R). 3) Decay estimates for the Carleman model on the real line and for the Carleman model in a box wiht reflecting boundary condintons.