Abstract
As a continuation of Section 2, the concept of parabolicity for Volterra equations of scalar type is introduced and resolvents for such equations are discussed in detail. If the kernel a(t) has some extra regularity property, like convexity, then the resolvent exists, and exhibits the same stability under perturbations as analytic resolvents. Again the maximal regularity property of type C α is valid, even for the perturbed equation. In Section 3.6 we derive a representation formula for the resolvent in case A is the generator of a Co-semigroup.
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© 1993 Springer Basel AG
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Prüss, J. (1993). Parabolic Equations. In: Evolutionary Integral Equations and Applications. Monographs in Mathematics, vol 87. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8570-6_3
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DOI: https://doi.org/10.1007/978-3-0348-8570-6_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-2876-4
Online ISBN: 978-3-0348-8570-6
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