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Regularity of solutions of nonlinear Volterra equations

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Nonlinear Evolution Equations and Related Topics

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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.

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Universität Essen, Essen, D-45117, Germany

    Volker G. Jakubowski

  2. UFR de Mathématiques, Université Louis Pasteur, Strasbourg, F-67084, France

    Petra Wittbold

Authors
  1. Volker G. Jakubowski
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  2. Petra Wittbold
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Editor information

Editors and Affiliations

  1. Department of Applied Analysis, University of Ulm, 89069, Ulm, Germany

    Wolfgang Arendt

  2. Analyse Numérique, Université Pierre et Marie Curie, B.C. 187, 4, place Jussieu, 75252, Paris Cedex 05, France

    Haïm Brézis

  3. Department of Mathematics Hill Center, Busch Campus, Rutgers University, 110 Frelinghuysen RD, Piscataway, NJ, 08854, USA

    Haïm Brézis

  4. Campus de Ker Lann, Antenne de Bretagne de l’ENS Cachan, 35170, Bruz, France

    Michel Pierre

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Dedicated to Philippe Bénilan

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© 2003 Springer Basel AG

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Jakubowski, V.G., Wittbold, P. (2003). Regularity of solutions of nonlinear Volterra equations. In: Arendt, W., Brézis, H., Pierre, M. (eds) Nonlinear Evolution Equations and Related Topics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7924-8_16

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  • DOI: https://doi.org/10.1007/978-3-0348-7924-8_16

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-7107-4

  • Online ISBN: 978-3-0348-7924-8

  • eBook Packages: Springer Book Archive

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