On a Mixed Problem for a Constant Coefficient Second-Order System
Via Millaures 12, 10146 Turin, Italy
Boundary Value Problems 2010, 2010:526917 doi:10.1155/2010/526917Published: 15 December 2010
The paper is devoted to the study of an initial boundary value problem for a linear second-order differential system with constant coefficients. The first part of the paper is concerned with the existence of the solution to a boundary value problem for the second-order differential system, in the strip , where is a suitable positive number. The result is proved by means of the same procedure followed in a previous paper to study the related initial value problem. Subsequently, we consider a mixed problem for the second-order constant coefficient system, where the space variable varies in and the time-variable belongs to the bounded interval , with sufficiently small in order that the operator satisfies suitable energy estimates. We obtain by superposition the existence of a solution , by studying two related mixed problems, whose solutions exist due to the results proved for the Cauchy problem in a previous paper and for the boundary value problem in the first part of this paper.