Acta applicandae mathematicae. 2025;196(1):4. doi: 10.1007/s10440-025-00717-x Q21.22024

[Formula: see text] Well-Posedness of Higher Order Hyperbolic Pseudo-Differential Equations with Multiplicities

带有多重性的高阶双曲型拟微分方程的“Well-Posedness”问题翻译改进

Claudia Garetto¹, Bolys Sabitbek^{2 3}

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作者单位

¹ School of Mathematical Sciences, Queen Mary University of London, Mile End Road, E1 4UJ London, UK.

² School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London, E1 4NS UK.

³ Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan.

DOI: 10.1007/s10440-025-00717-x PMID: 40028466

摘要 Ai翻译

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.

Keywords: Hyperbolic equations; Lower order terms; Multiplicities.

Keywords：multiplicities well-posedness

关键词：高阶双曲拟微分方程; 重根适定性