A Compact Course on Linear PDEs
Published on 12. January 2021
XIII, 235 pages
978-3-030-58205-0 (ISBN)
Description
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 some basic results on Fredholm alternative and spectral theory, some useful notes on functional analysis, a brief presentation of Sobolev spaces and their properties, saddle point problems, parabolic equations and hyperbolic equations. Many 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.
Reviews / Votes
"The book is designed to be compact, and it is - very. The author treats many topics very quickly, and the connecting links are also much abbreviated. A lot is demanded of the reader, even one starting with a background of classical PDEs at the undergraduate level." (Bill Satzer, MAA Reviews, December 27, 2021)More details
Series
Edition
1st ed. 2020
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Product notice
Reflowable
Illustrations
XIII, 235 p. 14 illus., 4 illus. in color.
ISBN-13
978-3-030-58205-0 (9783030582050)
DOI
10.1007/978-3-030-58205-0
Schweitzer Classification
Other editions
New editions
Alberto Valli
A Compact Course on Linear PDEs
E-Book
08/2023
2nd Edition
Springer
€69.54
Available for download
Additional editions
Alberto Valli
A Compact Course on Linear PDEs
Book
02/2021
Springer
€58.84
Article exhausted; check for reprint
Person
Alberto Valli is professor of Mathematical Analysis at the Department of Mathematics of the University of Trento. His research activity has concerned the analysis of partial differential equations in fluid dynamics and electromagnetism and of their numerical approximation by the finite element method. He also studied domain decomposition methods and their use in the discretization of partial differential equations. On these topics he wrote three books.
Content
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.- A Partition of unity.- B Lipschitz continuous and smooth domains.- C Integration by parts for smooth functions and vector ?elds.- D Reynolds transport theorem.- E Gronwall lemma.- F Necessary and su?cient conditions for the well-posedness of the variationalproblem.
