Compact Course on Linear PDEs

Häftad, Engelska, 2023

859 kr

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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.

Produktinformation

Utgivningsdatum2023-08-30
Mått155 x 235 x 15 mm
Vikt480 g
FormatHäftad
SpråkEngelska
SerieUNITEXT
Antal sidor262
Upplaga2
FörlagSpringer International Publishing AG
ISBN9783031359750

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Beräkning och matematisk analys inom Naturvetenskap och teknik

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.

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 ﬁelds.- Appendix D: Reynolds transport theorem.- Appendix E: Gronwall lemma.- Appendix F: Necessary and suﬃcient conditions for the well-posedness of the variational problem.