Regularity of solutions of nonlinear Volterra equations

Volker G. Jakubowski () and Petra Wittbold ()
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Volker G. Jakubowski: Universität Essen, Fachbereich Mathematik
Petra Wittbold: Université Louis Pasteur, UFR de Mathématiques

A chapter in Nonlinear Evolution Equations and Related Topics, 2003, pp 303-319 from Springer

Abstract: Abstract We consider the regularity properties of solutions of the nonlinear Volterra equation $$ \frac{d}{{dt}}\left( {u(t) - {u_{0}} + \int_{0}^{t} {k(t - s)(u(s) - {u_{0}})ds} } \right) + Au(t) \ni f(t) $$ in Banach spaces X without the Radon-Nikodym property. Existence of strong solutions for an m-completely accretive operator A in a normal Banach space X ⊂ L 1 (Ω;µ) is shown for sufficiently smooth data.

Keywords: 35D10; 45D05; 45N05; 47H06; Nonlinear Volterra equation; inhomogeneous Cauchy problem; regularity of solutions; completely accretive operators (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-7924-8_16

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DOI: 10.1007/978-3-0348-7924-8_16

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