A Compact Course on Linear PDEs
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 pro...
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| Tác giả chính: | |
|---|---|
| Tác giả của công ty: | |
| Định dạng: | Điện tử eBook |
| Ngôn ngữ: | Tiếng Anh |
| Được phát hành: |
Cham :
Springer International Publishing : Imprint: Springer,
2023.
|
| Phiên bản: | 2nd ed. 2023. |
| Loạt: | La Matematica per il 3+2,
154 |
| Những chủ đề: | |
| Truy cập trực tuyến: | https://doi.org/10.1007/978-3-031-35976-7 |
| Các nhãn: |
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| 100 | 1 | |a Valli, Alberto. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 2 | |a A Compact Course on Linear PDEs |h [electronic resource] / |c by Alberto Valli. |
| 250 | |a 2nd ed. 2023. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2023. | |
| 300 | |a 1 online resource (XV, 262 p. 13 illus.). |b 4 illus. in color. | ||
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| 490 | 1 | |a La Matematica per il 3+2, |x 2038-5757 ; |v 154 | |
| 505 | 0 | |a 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. | |
| 520 | |a 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. . | ||
| 532 | 8 | |a Accessibility summary: This PDF does Not fully comply with PDF/UA standards but does include limited screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility | |
| 532 | 8 | |a Inaccessible, or known limited accessibility | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Mathematics |x Data processing. | |
| 650 | 0 | |a Functional analysis. | |
| 650 | 1 | 4 | |a Differential Equations. |
| 650 | 2 | 4 | |a Computational Mathematics and Numerical Analysis. |
| 650 | 2 | 4 | |a Functional Analysis. |
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