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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2405.04927 |
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| _version_ | 1866916239203368960 |
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| author | Garetto, Claudia Sabitbek, Bolys |
| author_facet | Garetto, Claudia Sabitbek, Bolys |
| contents | In this paper, we study higher order hyperbolic pseudo-differential equations with variable multiplicities. We work in arbitrary space dimension and we assume that the principal part is time-dependent only. We identify sufficient conditions on the roots and the lower order terms (Levi conditions) under which the corresponding Cauchy problem is $C^\infty$ well-posed. This is achieved via transformation into a first order system, reduction into upper-triangular form and application of suitable Fourier integral operator methods previously developed for hyperbolic non-diagonalisable systems. We also discuss how our result compares with the literature on second and third order hyperbolic equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04927 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $C^\infty$ well-posedness of higher order hyperbolic pseudo-differential equations with multiplicities Garetto, Claudia Sabitbek, Bolys Analysis of PDEs 35L25, 35L30 In this paper, we study higher order hyperbolic pseudo-differential equations with variable multiplicities. We work in arbitrary space dimension and we assume that the principal part is time-dependent only. We identify sufficient conditions on the roots and the lower order terms (Levi conditions) under which the corresponding Cauchy problem is $C^\infty$ well-posed. This is achieved via transformation into a first order system, reduction into upper-triangular form and application of suitable Fourier integral operator methods previously developed for hyperbolic non-diagonalisable systems. We also discuss how our result compares with the literature on second and third order hyperbolic equations. |
| title | $C^\infty$ well-posedness of higher order hyperbolic pseudo-differential equations with multiplicities |
| topic | Analysis of PDEs 35L25, 35L30 |
| url | https://arxiv.org/abs/2405.04927 |