The generalized solutions of the Lama's equations in the case of running loads. The shock waves

TL;DR

This paper investigates Lama's equations for elastic media under various velocities, focusing on shock wave formation and providing a method to determine conditions on solutions across shock fronts using generalized functions.

Contribution

It introduces a novel method based on generalized functions theory to analyze solutions of Lama's equations with shock waves in elastic media.

Findings

Derived conditions for solutions across shock fronts.

Extended solutions to include subsonic, transonic, and supersonic regimes.

Provided a framework for analyzing shock wave effects in elastic media.

Abstract

The system of Lama's equations is investigated, describing the motion of the elastic media under subsonic, transonic and supersonic velocities of the moving source of distributions, and its decisions in space of generalized vector-functions. The questions are considered connected with arising shock waves, which appear in ambience under supersonic source of distributions. On base of the generalized functions theories the method of the determination of the conditions on gaps of the decisions and their derivatives on shock waves fronts is offered.