Compact Course on Linear PDEs

AvAlberto Valli

Häftad, Engelska, 2023

Del 154 i serien UNITEXT

711 kr

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Beskrivning

This textbook is devoted to second order linear partial differential equations. The focus is on variational formulations in Hilbert spaces. 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. Almost 80 exercises are added, and the complete solution of all of them is included. The work is mainly addressed to students in Mathematics, but also students in Engineering with a good mathematical background should be able to follow the theory presented here. This second edition has been enriched by some new sections and new exercises; in particular, three important equations are now included: the biharmonic equation, the linear Navier-Stokes equations and the Maxwell equations.

Produktinformation

Utgivningsdatum:2023-08-30
Mått:155 x 235 x 15 mm
Vikt:480 g
Format:Häftad
Språk:Engelska
Serie:UNITEXT
Antal sidor:262
Upplaga:2
Förlag:Springer International Publishing AG
ISBN:9783031359750

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Mer om författaren

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.

Innehållsförteckning

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.