The Cauchy problem for p-evolution equations with initial data in Gelfand-Shilov spaces

2025/10/23 by Marco Cappiello, Cappiello, Marco, Eliakim Cleyton Machado +1
Mathematics · #35B65 #35G10 #35S05 #46F05 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2510.20702

openalex publication_date 2025/10/23 · openalex created_date 2025/10/25 · openalex updated_date 2026/08/04

Abstract

We study the Cauchy problem for a class of linear evolution equations of arbitrary order with coefficients depending both on time and space variables. Under suitable decay assumptions on the coefficients of the lower order terms for |x| large, we prove a well-posedness result in Gelfand-Shilov spaces.

Citations

• Polynomially oscillatory multipliers on Gelfand-Shilov spaces
• The Cauchy problem for p-evolution equations with variable coefficients in Gevrey classes
• On the Cauchy problem for p-evolution equations with variable coefficients: a necessary condition for Gevrey well-posedness
• Gevrey well posedness for 3-evolution equations with variable coefficients
• The Cauchy problem for 3-evolution equations with data in Gelfand-Shilov spaces
• Schrödinger-type equations in Gelfand-Shilov spaces

Related

• The Cauchy problem for p-evolution equations with variable coefficients in Gevrey classes
• On the Cauchy problem for p-evolution equations with variable coefficients: a necessary condition for Gevrey well-posedness
• The Cauchy problem for 3-evolution equations with data in Gelfand-Shilov spaces
• Some remarks on the Cauchy Problem for Schrödinger type equations in Gelfand-Shilov spaces
• Globally solvable time-periodic evolution equations in Gelfand-Shilov classes