Regularity properties for evolution family governed by non-autonomous forms

2017/06/20 by Hafida Laasri, Laasri, Hafida
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1706.06340

openalex publication_date 2017/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper gives further regularity properties of the evolution family associated with a non-autonomous evolution equation u(t)+A(t)u(t)=f(t), t∈[0,T], u(0)=u₀, where A(t), t∈ [0,T], arise from non-autonomous sesquilinear forms \mathfrak a(t,⋅,⋅) on a Hilbert space H with constant domain V⊂ H. Results on norm continuity, compactness and results on the Gibbs character of the evolution family are established. The abstract results are applied to the Laplacian operator with time dependent Robin boundary conditions.

Citations

• One-parameter semigroups for linear evolution equations

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