# Delta Waves for a Strongly Singular Initial-Boundary Hyperbolic Problem with Integral Boundary Condition

### Irina Kmit

Mechanics and Mathematics, Lviv, Ukraine

## Abstract

We investigate the existence and the singular structure of delta wave solutions to a semilinear hyperbolic equation with strongly singular initial and boundary conditions. The boundary conditions are given in nonlocal form with a linear integral operator involved. We construct a delta wave solution as a distributional limit of solutions to the regularized system. This determines the macroscopic behavior of the corresponding generalized solution in the Colombeau algebra G of generalized functions. We represent our delta wave as a sum of a purely singular part satisfying a linear system and a regular part satisfying a nonlinear system.

## Cite this article

Irina Kmit, Delta Waves for a Strongly Singular Initial-Boundary Hyperbolic Problem with Integral Boundary Condition. Z. Anal. Anwend. 24 (2005), no. 1, pp. 29–74

DOI 10.4171/ZAA/1229