Bulletin of the Australian Mathematical Society, ( ISI ), Volume (69), No (1), Year (2004-11) , Pages (383-384)

Title : ( ON THE n-PARAMETER ABSTRACT CAUCHY PROBLEM )

Authors: Mohammad Janfada , Assadollah Niknam ,

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Let H{(i = 1,2,..., n), be closed operators in a Banach space X. The generalised initial value problem Q£ufa,t2,...,ti,...,tn) = Haifa,...,tn), <i£(0,Ti] i = l , 2 , . . . , n | u(0) = x, x e n D{Hi), of the abstract Cauchy problem is studied. We show that the uniqueness of solution u : [0,Ti] x [0,T2] x • • • x [0,Tn] -• X of this n-abstract Cauchy problem is closely related to Co-n-parameter semigroups of bounded linear operators on X. Also as another application of Cb-n-parameter semigroups, we prove that many n-parameter initial value problems cannot have a unique solution for some initial values.

Keywords

, n-parameter semi-group, Cauchy
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@article{paperid:1027129,
author = {Janfada, Mohammad and Niknam, Assadollah},
title = {ON THE n-PARAMETER ABSTRACT CAUCHY PROBLEM},
journal = {Bulletin of the Australian Mathematical Society},
year = {2004},
volume = {69},
number = {1},
month = {November},
issn = {0004-9727},
pages = {383--384},
numpages = {1},
keywords = {n-parameter semi-group; Cauchy problem;},
}

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%0 Journal Article
%T ON THE n-PARAMETER ABSTRACT CAUCHY PROBLEM
%A Janfada, Mohammad
%A Niknam, Assadollah
%J Bulletin of the Australian Mathematical Society
%@ 0004-9727
%D 2004

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