Showing a limited preview of this publication:
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.
Key words.: Degenerate in time differential equations in Banach spaces; Representation formulae for direct and inverse problems; Application to parabolic PDE's
Received: 2008-08-28
Published Online: 2009-07-06
Published in Print: 2009-July
© de Gruyter 2009