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

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

2004-01-31

arxiv.org/abs/math/0402003v1

Mathematics

Analysis of PDEs

42 pages

Scientific paper

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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