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Non autonomous evolution operators of hyperbolic type

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Abstract

In this paper we consider a Cauchy problem in a Banach spaceE:u′(t)=A(t)u(t)+f(t), t∈[t 0, T], u(t0)=u0, whereA(·) is a family of linear operators inE which satisfy all the requirements of Kato's semigroup approach to the non autonomous hyperbolic equations except for the density of the common domains ofA(t). An application is given to a hyperbolic partial differential equation with discontinuous coefficients.

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Authors and Affiliations

  1. Scuola Normale di Pisa, 56126, Pisa, Italy

    Giuseppe Da Prato & Eugenio Sinestrari

  2. Dipartimento di Matematica, Universitá di Roma I, Piazzale Aldo Moro 2, 00185, Roma, Italy

    Giuseppe Da Prato & Eugenio Sinestrari

Authors
  1. Giuseppe Da Prato
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  2. Eugenio Sinestrari
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Additional information

Communicated by R. Nagel

Partially supported by the Italian National Project M. P. I. “Equazioni di Evoluzione e Applicazioni Fisico-Matematiche”

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Da Prato, G., Sinestrari, E. Non autonomous evolution operators of hyperbolic type. Semigroup Forum 45, 302–321 (1992). https://doi.org/10.1007/BF03025772

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  • DOI: https://doi.org/10.1007/BF03025772

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