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

2004/01/31 by Kmit, Irina
#35L50 #35L60 #58J47 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0402003

Abstract

We investigate the existence and the singular structure of delta wave solutions to a semilinear strictly 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.

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