Hyperbolic differential-operator equations on a whole axis
The author considers the initial-boundary value problem for hyperbolic equations on the whole axis such that a part of the initial-boundary conditions contains the differentiation in time. Actually, an abstract interpretation of this problem is given. As application, he gives sufficient conditions under which the solution of the problem is stable. In particular, the method given in this paper, is applied to study the longitudinal displacements of an inhomogeneous rod under the action of forces at the two ends which are proportional to the acceleration.
scientific article; zbMATH DE number 2163640