Boundary and Initial-Value Problems for Equations of Hyperbolic and Parabolic Type in Two Independent Variables

Abstract

In Most Applications the pure initial-value problem is not the center of interest; usually, suitable boundary conditions are added which are distinguished in their great variety. The simplest examples were mentioned in Sections I-2.3 and I-4.4. Among the methods for treating such problems, we mentioned the separation method, with which the reader will certainly be familiar in the case of simple problems, and the calculus of Laplace transforms, which to a great extent takes into account the group or semigroup character of the solution operator. We shall justify this calculus to a modest extent.