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A Compact Course on Linear PDEs

BuchKartoniert, Paperback
262 Seiten
Englisch
Springererschienen am30.08.20232. Aufl.
It contains elliptic equations, including the biharmonic problem, some useful notes on functional analysis, a brief presentation of Sobolev spaces and their properties, some basic results on Fredholm alternative and spectral theory, saddle point problems, parabolic and linear Navier-Stokes equations, and hyperbolic and Maxwell equations.mehr
Verfügbare Formate
BuchKartoniert, Paperback
EUR64,19
E-BookPDF1 - PDF WatermarkE-Book
EUR58,84
E-BookPDF1 - PDF WatermarkE-Book
EUR64,19

Produkt

KlappentextIt contains elliptic equations, including the biharmonic problem, some useful notes on functional analysis, a brief presentation of Sobolev spaces and their properties, some basic results on Fredholm alternative and spectral theory, saddle point problems, parabolic and linear Navier-Stokes equations, and hyperbolic and Maxwell equations.
Details
ISBN/GTIN978-3-031-35975-0
ProduktartBuch
EinbandartKartoniert, Paperback
Verlag
Erscheinungsjahr2023
Erscheinungsdatum30.08.2023
Auflage2. Aufl.
ReiheUNITEXT
Seiten262 Seiten
SpracheEnglisch
IllustrationenXV, 262 p. 13 illus., 4 illus. in color.
Artikel-Nr.54058262

Inhalt/Kritik

Inhaltsverzeichnis
1. Introduction.- 2. Second order linear elliptic equations.- 3. A bit of functional analysis.- 4. Weak derivatives and Sobolev spaces.- 5. Weak formulation of elliptic PDEs.- 6. Technical results.- 7. Additional results.- 8. Saddle points problems.- 9. Parabolic PDEs.- 10. Hyperbolic PDEs.- Appendix A: Partition of unity.- Appendix B: Lipschitz continuous and smooth domains.- Appendix C: Integration by parts for smooth functions and vector ï¬elds.- Appendix D: Reynolds transport theorem.- Appendix E: Gronwall lemma.- Appendix F: Necessary and suï¬cient conditions for the well-posedness of the variational problem.mehr

Schlagworte

Autor

Alberto Valli is a Professor of Mathematical Analysis at University of Trento. His research activity has focused on the mathematical analysis of linear and nonlinear partial differential equations, in particular in fluid dynamics and electromagnetism, and on their numerical approximation by means of the finite element method. He published more than 80 papers in prestigious international journals and 4 books on partial differential equations and their numerical approximation.