東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

A compact course on linear PDEs

Valli, A.

Linked to FindBook

Google Book

Amazon

博客來

A compact course on linear PDEs

Record Type:	Electronic resources : Monograph/item
Title/Author:	A compact course on linear PDEs/ by Alberto Valli.
Author:	Valli, A.
Published:	Cham :Springer International Publishing : : 2023.,
Description:	xv, 262 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Functional Analysis. -
Online resource:	https://doi.org/10.1007/978-3-031-35976-7
ISBN:	9783031359767

A compact course on linear PDEs
Valli, A.

A compact course on linear PDEs[electronic resource] /by Alberto Valli. - Second edition. - Cham :Springer International Publishing :2023. - xv, 262 p. :ill., digital ;24 cm. - La matematica per il 3+2,v. 1542038-5757 ;. - La matematica per il 3+2 ;v. 154..

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.

ISBN: 9783031359767

Standard No.: 10.1007/978-3-031-35976-7doiSubjects--Topical Terms:

893943
Functional Analysis.

LC Class. No.: QA320 / .V35 2023

Dewey Class. No.: 515.353

A compact course on linear PDEs
LDR:02656nmm a2200349 a 4500 001 2334083
003 DE-He213
005 20230829202436.0
006 m d
007 cr nn 008maaau
008 240402s2023 sz s 0 eng d
020 $a 9783031359767 $q (electronic bk.)
020 $a 9783031359750 $q (paper)
024 7 $a 10.1007/978-3-031-35976-7 $2 doi
035 $a 978-3-031-35976-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA320 $b .V35 2023
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.353 $2 23
090 $a QA320 $b .V188 2023
100 1 $a Valli, A. $3 3665380
245 1 2 $a A compact course on linear PDEs $h [electronic resource] / $c by Alberto Valli.
250 $a Second edition.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2023.
300 $a xv, 262 p. : $b ill., digital ; $c 24 cm.
490 1 $a La matematica per il 3+2, $x 2038-5757 ; $v 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.
650 2 4 $a Functional Analysis. $3 893943
650 0 $a Differential equations, Partial. $3 518115
650 0 $a Functional analysis. $3 531838
650 1 4 $a Differential Equations. $3 907890
650 2 4 $a Computational Mathematics and Numerical Analysis. $3 891040
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a La matematica per il 3+2 ; $v v. 154. $3 3665381
856 4 0 $u https://doi.org/10.1007/978-3-031-35976-7
950 $a Mathematics and Statistics (SpringerNature-11649)