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arXiv · 1706.06340

Regularity properties for evolution family governed by non-autonomous forms

Hafida Laasri
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Abstract

This paper gives further regularity properties of the evolution family associated with a non-autonomous evolution equation \begin{equation*}\label{Abstract equation} \dot u(t)+A(t)u(t)=f(t),\ \ t\in[0,T],\ \ u(0)=u_0, \end{equation*} where $A(t),\ t\in [0,T],$ arise from non-autonomous sesquilinear forms $\mathfrak a(t,\cdot,\cdot)$ on a Hilbert space $H$ with constant domain $V\subset H.$ Results on norm continuity, compactness and results on the \textit{Gibbs} character of the evolution family are established. The abstract results are applied to the Laplacian operator with time dependent Robin boundary conditions.

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Hafida Laasri. 2017-06-20. Regularity properties for evolution family governed by non-autonomous forms. https://arxiv.org/abs/1706.06340

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