Boundary value problems for evolution partial differential equations with discontinuous data

TL;DR

This paper analyzes how solutions to linear evolution PDEs on the half line behave with discontinuous initial or boundary data and corner singularities, providing a characterization via special functions.

Contribution

It introduces a new characterization of solutions involving an expansion in terms of computable special functions for PDEs with discontinuities.

Findings

Solutions can be expanded using special functions

Discontinuous data significantly affect solution behavior

Corner singularities are explicitly characterized

Abstract

We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the solutions in the presence of corner singularities. The characterization focuses on an expansion in terms of computable special functions.