An integral evolution formula of boundary value problem for wave equations

Abstract

This article proposes a new integral evolution formula of boundary value problem for wave equations of the form utt(x,t)+L(x,D)u(x,t)=f(x,t). By introducing the operator functions, e.g., ϕ-functions, and using the Duhamel’s principle, a compact integral evolution formula is established for inhomogeneous wave equations. The derivation is based on Duhamel’s principle and the theory of operational calculus.