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arXiv · 1608.07079

Variation of constants formula and exponential dichotomy for non autonomous non densely defined Cauchy problems

Pierre Magal·Ousmane Seydi
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Abstract

In this paper we prove a variation of constants formula for a non autonomous and non homogeneous Cauchy problems whenever the linear part is not densely defined and is not a Hille-Yosida operator. By using this variation of constants formula we derive a necessary and sufficient conditions for the existence of exponential dichotomy for the evolution family generated by the associated non autonomous homogeneous problem. We also prove a persistence result of the exponential dichotomy for small perturbations. Finally we illustrate our result by consider a parabolic equation with non local and non autonomous boundary conditions.

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Pierre Magal, Ousmane Seydi. 2016-08-25. Variation of constants formula and exponential dichotomy for non autonomous non densely defined Cauchy problems. https://arxiv.org/abs/1608.07079

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