Maximal Regularity for Non-Autonomous Second Order Cauchy Problems

2013/11/08 by Dominik Dier, Dier, Dominik, El Maati Ouhabaz +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.1311.1902

openalex publication_date 2013/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider non-autonomous wave equations \ \beginaligned & u(t) + \B(t) u(t) + \A(t)u(t) = f(t) t-a.e.
&u(0)=u₀, u(0) = u₁. \endaligned . where the operators \A(t) and \B(t) are associated with time-dependent sesquilinear forms \fra(t,.,.) and \frb defined on a Hilbert space H with the same domain V. The initial values satisfy u₀ ∈ V and u₁ ∈ H. We prove well-posedness and maximal regularity for the solution both in the spaces V' and H. We apply the results to non-autonomous Robin-boundary conditions and also use maximal regularity to solve a quasilinear problem.

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

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