A question on the Cauchy problem in the Gevrey classes for weakly hyperbolic equations

2022/10/05 by Tatsuo Nishitani, Nishitani, Tatsuo
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Analysis and Transform Methods #math.AP

paper · pdf · doi:10.48550/arxiv.2210.02605

5 pages

arxiv created 2022/10/05 · openalex publication_date 2022/10/05 · arxiv updated 2022/10/07 · openalex created_date 2022/10/08 · openalex updated_date 2026/07/28

Abstract

For a homogeneous polynomial p in ξ∈ \bf Rⁿ with Gevrey coefficients, it is known that the Cauchy problem for any realization of p is well-posed in the Gevrey class of order s<2 if the characteristic roots are real. In this note, we give examples showing the situation of the converse direction, in particular the optimality of the Gevrey order s=2.

Related

• On hyperbolicity and Gevrey well-posedness. Part three: a class of weakly hyperbolic systems
• On the Gevrey strong hyperbolicity
• The Cauchy problem for p-evolution equations with variable coefficients in Gevrey classes
• On hyperbolicity and Gevrey well-posedness. Part one: the elliptic case
• Counterexamples to C^∞ well posedness for some hyperbolic operators with triple characteristics