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＜電子ブック＞
A Compact Course on Linear PDEs / by Alberto Valli
(La Matematica per il 3+2. ISSN:20385757 ; 154)

版	2nd ed. 2023.
出版者	Cham : Springer International Publishing : Imprint: Springer
出版年	2023
本文言語	英語
大きさ	XV, 262 p. 13 illus., 4 illus. in color : online resource
著者標目	*Valli, Alberto author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Functional analysis FREE:Differential Equations FREE:Computational Mathematics and Numerical Analysis FREE:Functional Analysis
一般注記	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 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. HTTP:URL=https://doi.org/10.1007/978-3-031-35976-7

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