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On the n-parameter abstract Cauchy problem

Published online by Cambridge University Press:  17 April 2009

M. Janfada  and
A. Niknam
M. Janfada
Affiliation:
Department of Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Masjad, Iran, e-mail: Niknam@math.um.ac.ir, Janfada@math.um.ac.ir
A. Niknam
Affiliation:
Department of Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Masjad, Iran, e-mail: Niknam@math.um.ac.ir, Janfada@math.um.ac.ir
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Let Hi(i = 1, 2, …, n), be closed operators in a Banach space X. The generalised initialvalue problem

of the abstract Cauchy problem is studied. We show that the uniqueness of solution u: [0, T1] × [0, T2] × … × [0, Tn] → X of this n-abstract Cauchy problem is closely related to C0-n-parameter semigroups of bounded linear operators on X. Also as another application of C0-n-parameter semigroups, we prove that many n-parameter initial value problems cannot have a unique solution for some initial values.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 3 , June 2004 , pp. 383 - 394
Copyright
Copyright © Australian Mathematical Society 2004

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