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A Compact Course on Linear PDEs
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A Compact Course on Linear PDEs
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
A Compact Course on Linear PDEs/ by Alberto Valli.
作者:
Valli, Alberto.
面頁冊數:
XIII, 235 p. 14 illus., 4 illus. in color.online resource. :
Contained By:
Springer Nature eBook
標題:
Functional Analysis. -
電子資源:
https://doi.org/10.1007/978-3-030-58205-0
ISBN:
9783030582050
A Compact Course on Linear PDEs
Valli, Alberto.
A Compact Course on Linear PDEs
[electronic resource] /by Alberto Valli. - 1st ed. 2020. - XIII, 235 p. 14 illus., 4 illus. in color.online resource. - La Matematica per il 3+2,1262038-5722 ;. - La Matematica per il 3+2,84.
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 fields -- D Reynolds transport theorem -- E Gronwall lemma -- F Necessary and sufficient conditions for the well-posedness of the variationalproblem.
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.
ISBN: 9783030582050
Standard No.: 10.1007/978-3-030-58205-0doiSubjects--Topical Terms:
672166
Functional Analysis.
LC Class. No.: QA370-380
Dewey Class. No.: 515.353
A Compact Course on Linear PDEs
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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 fields -- D Reynolds transport theorem -- E Gronwall lemma -- F Necessary and sufficient conditions for the well-posedness of the variationalproblem.
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