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# Zeitschrift für Analysis und ihre Anwendungen

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**Volume 24, Issue 1, 2005, pp. 29–74**

**DOI: 10.4171/ZAA/1229**

Published online: 2005-03-31

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

Irina Kmit^{[1]}(1) Mechanics and Mathematics, Lviv, Ukraine

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.

*Keywords: *Hyperbolic equation, integral condition, strongly singular data, delta wave, population dynamics

Kmit Irina: Delta Waves for a Strongly Singular Initial-Boundary Hyperbolic Problem with Integral Boundary Condition. *Z. Anal. Anwend.* 24 (2005), 29-74. doi: 10.4171/ZAA/1229