C∞ Well-Posedness of Higher Order Hyperbolic Pseudo-Differential Equations with Multiplicities
Garetto C. Sabitbek B.
April 2025Springer Science and Business Media B.V.
Acta Applicandae Mathematicae
2025#196Issue 1
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∞ 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.
Hyperbolic equations , Lower order terms , Multiplicities
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School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London, E1 4UJ, United Kingdom
School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London, E1 4NS, United Kingdom
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
School of Mathematical Sciences
School of Mathematical Sciences
Institute of Mathematics and Mathematical Modeling
10 лет помогаем публиковать статьи Международный издатель
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