Non-homogeneous problem for the fractional wave equation with irregular coefficients and data
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909535192481792 |
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| author | Bouguenna, Manel Sebih, Mohammed Elamine |
| author_facet | Bouguenna, Manel Sebih, Mohammed Elamine |
| contents | In this paper, we consider the Cauchy problem for a non-homogeneous wave equation generated by the fractional Laplacian and involving different kinds of lower order terms. We allow the equation coefficients and data to be of distributional type or less regular, having in mind the Dirac delta function and its powers, and we prove that the problem is well-posed in the sense of the concept of very weak solutions. Moreover, we prove the uniqueness in an appropriate sense and the coherence of the very weak solution concept with classical theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07912 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-homogeneous problem for the fractional wave equation with irregular coefficients and data Bouguenna, Manel Sebih, Mohammed Elamine Analysis of PDEs 35L81, 35L05, 35D30, 35A35 In this paper, we consider the Cauchy problem for a non-homogeneous wave equation generated by the fractional Laplacian and involving different kinds of lower order terms. We allow the equation coefficients and data to be of distributional type or less regular, having in mind the Dirac delta function and its powers, and we prove that the problem is well-posed in the sense of the concept of very weak solutions. Moreover, we prove the uniqueness in an appropriate sense and the coherence of the very weak solution concept with classical theory. |
| title | Non-homogeneous problem for the fractional wave equation with irregular coefficients and data |
| topic | Analysis of PDEs 35L81, 35L05, 35D30, 35A35 |
| url | https://arxiv.org/abs/2503.07912 |