ON THE WELLPOSEDNESS OF NONAUTONOMOUS SECOND ORDER CAUCHY PROBLEMS

Abstract

We study the existence and uniqueness of classical solutions to the following nonautonomous second order Cauchy problem u(t)=A(t)u(t)+B(t)u(t)+f(t), 0 ≤ s≤ t≤ T, u(0) = u0 ∈ E,u(0) = u1 ∈ E, by using operator matrices and then give applications to partial differential equations.