Analytic Semigroups and Optimal Regularity in Parabolic Problems
Seiten
1995
Springer Basel (Verlag)
978-3-7643-5172-4 (ISBN)
Springer Basel (Verlag)
978-3-7643-5172-4 (ISBN)
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The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems.
Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones.
Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived.
The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in parabolic partial differential equations and systems. It gives a comprehensive overview on the present state of the art in the field, teaching at the same time how to exploit its basic techniques.
Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones.
Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived.
The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in parabolic partial differential equations and systems. It gives a comprehensive overview on the present state of the art in the field, teaching at the same time how to exploit its basic techniques.
Alessandra Lunardi is a professor of mathematics at the University of Parma, Italy.
Introduction.- 0 Preliminary material: spaces of continuous and Hölder continuous functions.- 1 Interpolation theory.- Analytic semigroups and intermediate spaces.- 3 Generation of analytic semigroups by elliptic operators.- 4 Nonhomogeneous equations.- 5 Linear parabolic problems.- 6 Linear nonautonomous equations.- 7 Semilinear equations.- 8 Fully nonlinear equations.- 9 Asymptotic behavior in fully nonlinear equations.- Appendix: Spectrum and resolvent.- Bibliography.- Index.
Erscheint lt. Verlag | 30.6.2009 |
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Reihe/Serie | Progress in Nonlinear Differential Equations and Their Applications |
Sprache | englisch |
Maße | 155 x 235 mm |
Gewicht | 807 g |
Einbandart | gebunden |
Schlagworte | Analysis • Evolution Equations |
ISBN-10 | 3-7643-5172-1 / 3764351721 |
ISBN-13 | 978-3-7643-5172-4 / 9783764351724 |
Zustand | Neuware |
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