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Licensed Unlicensed Requires Authentication Published by De Gruyter July 6, 2009

Representation formulae for solutions to direct and inverse degenerate in time first-order Cauchy problems in Banach spaces

  • A. Lorenzi

Abstract

We are concerned with a degenerate in time first-order identification problem related to a closed operator in a Banach space. The degeneracy with respect to time — due to scalar time coefficients — is assumed to be integrable. For both direct and inverse problem we exhibit explicit representations of the solutions in terms of the linear operator A and function ƒ (cf. equation (1.1)), when the latter possess specific properties.

Some applications to partial differential equations are given.

Received: 2008-08-28
Published Online: 2009-07-06
Published in Print: 2009-July

© de Gruyter 2009

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