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1995 Nonautonomous integro-differential equations of hyperbolic type
Hirokazu Oka, Naoki Tanaka
Differential Integral Equations 8(7): 1823-1831 (1995).

Abstract

This paper is devoted to two problems for the nonautonomous integrodifferential equation in a Banach space $X$ of hyperbolic type $$ \text{$u'(t) = A(t)u(t)+ \int_0^t B(t,s)u(s) ds + f(t)$ for $t\in[0,T]$, and $u(0) = u_0$.} $$ One is the problem of existence and uniqueness of classical solutions without assuming that the common domain of $A(t)$ is dense in $X$, and the other is the regularity problem in the case where the common domain of $A(t)$ is dense in $X$. The regularity result will play a role in developing an abstract theory which can be applied to the second-order integrodifferential equations with the third kind boundary conditions.

Citation

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Hirokazu Oka. Naoki Tanaka. "Nonautonomous integro-differential equations of hyperbolic type." Differential Integral Equations 8 (7) 1823 - 1831, 1995.

Information

Published: 1995
First available in Project Euclid: 12 May 2013

zbMATH: 0826.45006
MathSciNet: MR1347983

Subjects:
Primary: 45N05
Secondary: 34K30

Rights: Copyright © 1995 Khayyam Publishing, Inc.

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Vol.8 • No. 7 • 1995
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