Application of the Laplace transform method to wave motions involving strong discontinuities

Abstract

AbstractFormulae are obtained for the Laplace transforms of the first and second partial derivatives of a function of time and position which, together with its first partial derivatives, is discontinuous on a moving surface. These formulae are then used in a discussion of the application of the Laplace transform method to the solution of mixed initial and boundary-value problems in linear thermoelasticity. Particular attention is given to thermoelastic disturbances involving plane shock waves, and it is pointed out that no properly posed formulation of problems of this type has yet been found.