| Autor: |
Garetto, Claudia, Sabitbek, Bolys |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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