Abstract
The abstract theory of linear parabolic problems, developed in the first part of this treatise, rests on two cornerstones: on the theory of analytic semigroups and on interpolation theory. In the first section of this chapter we discuss in some detail the classes of generators of analytic semigroups that are used throughout. In the second section we review the fundamentals of interpolation theory. We also introduce the class of ‘admissible interpolation functors’ that, on the one hand, is flexible enough to build an easy and general abstract theory of evolution equations on it, and, on the other hand, is general enough to cover all applications occurring in practice.
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© 1995 Birkhäuser Verlag Basel
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Amann, H. (1995). Generators and Interpolation. In: Linear and Quasilinear Parabolic Problems. Monographs in Mathematics, vol 89. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9221-6_2
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DOI: https://doi.org/10.1007/978-3-0348-9221-6_2
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9950-5
Online ISBN: 978-3-0348-9221-6
eBook Packages: Springer Book Archive