Generalized solutions for the abstract singular Cauchy problem

Hernan R. Henriquez

doi:10.3934/cpaa.2009.8.955

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2009, Volume 8, Issue 3: 955-976. Doi: 10.3934/cpaa.2009.8.955

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Generalized solutions for the abstract singular Cauchy problem

Hernan R. Henriquez¹

1.
Departamento de Matemática, Universidad de Santiago, USACH, Casilla 307, Correo-2, Santiago

Received: February 29, 2008

Revised: July 31, 2008

Published: April 2009

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Abstract

In this work we study existence of solutions in convoluted sense for the abstract singular Cauchy problem. We relate the existence of convoluted solutions with the existence of a generalized singular evolution operator, and we establish a Hille-Yosida type theorem to characterize the existence of a local generalized singular evolution operator.

Keywords:

Abstract singular Cauchy problem,
generalized singular evolution operator,
Laplace transform.

Mathematics Subject Classification: Primary: 34G10, 35K65; Secondary: 47D62.

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