Perturbations of non-autonomous second-order abstract Cauchy problems

2023/02/22 by Christian Budde, Christian Seifert, Budde, Christian +1 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2302.11270

openalex publication_date 2023/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we present time-dependent perturbations of second-order non-autonomous abstract Cauchy problems associated to a family of operators with constant domain. We make use of the equivalence to a first-order non-autonomous abstract Cauchy problem in a product space, which we elaborate in full detail. As an application we provide a perturbed non-autonomous wave equation.

Cited by

• Solutions to Second-Order Nonlocal Evolution Equations Governed by Non-Autonomous Forms

Related

• Perturbations of non-autonomous second-order abstract Cauchy problems
• Non-autonomous Desch-Schappacher perturbations
• Maximal Regularity for Non-Autonomous Second Order Cauchy Problems
• Solution Operator for Non-Autonomous Perturbation of Gibbs Semigroup
• Non-autonomous right and left multiplicative perturbations and maximal regularity