Linear Hyperbolic Functional-Differential Equations with Essentially Bounded Right-Hand Side

Abstract EN

Theorems on the unique solvability and nonnegativity of solutions to the characteristic initial value problem u1,1(t,x)=l0(u)(t,x)+l1(u1,0)(t,x)+l2(u0,1)(t,x)+q(t,x), u(t,c)=α(t) for t∈[a,b], u(a,x)=β(x) for x∈[c,d] given on the rectangle [a,b]×[c,d] are established, where the linear operators l0, l1, l2 map suitable function spaces into the space of essentially bounded functions.

General results are applied to the hyperbolic equations with essentially bounded coefficients and argument deviations.