Delta Waves for a Strongly Singular Initial-Boundary Hyperbolic Problem with Integral Boundary Condition
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arXiv
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| Format: | Preprint |
| Published: |
2004
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| _version_ | 1866908702340022272 |
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| author | Kmit, Irina |
| author_facet | Kmit, Irina |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0402003 |
| institution | arXiv |
| publishDate | 2004 |
| record_format | arxiv |
| spellingShingle | Delta Waves for a Strongly Singular Initial-Boundary Hyperbolic Problem with Integral Boundary Condition Kmit, Irina Analysis of PDEs 35L50, 35L60, 58J47 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. |
| title | Delta Waves for a Strongly Singular Initial-Boundary Hyperbolic Problem with Integral Boundary Condition |
| topic | Analysis of PDEs 35L50, 35L60, 58J47 |
| url | https://arxiv.org/abs/math/0402003 |