Representation and approximation of solutions to semilinear Volterra equations with delay |
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Authors: | WE Fitzgibbon |
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Institution: | Department of Mathematics, University of Houston, Houston, Texas 77004 U.S.A. |
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Abstract: | In this paper we use a theorem of Crandall and Pazy to provide the product integral representation of the nonlinear evolution operator associated with solutions to the semilinear Volterra equation: x(?)(t) = W(t, τ) ?(0) + ∝τtW(t, s)F(s, xs(?)) ds.Here the kernel W(t, s) is a linear evolution operator on a Banach space X; I is an interval of the form ?r, 0] or (?∞, 0] and F is a nonlinear mapping of R × C(I, X) into X. The abstract theory is applied to examples of partial functional differential equations. |
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