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Books on the topic 'Geometric PDEs'

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Author: Grafiati

Published: 14 March 2023

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1

Gursky, Matthew J., Ermanno Lanconelli, Andrea Malchiodi, Gabriella Tarantello, Xu-Jia Wang, and Paul C. Yang. Geometric Analysis and PDEs. Edited by Sun-Yung Alice Chang, Antonio Ambrosetti, and Andrea Malchiodi. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-01674-5.

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2

Ponce, Augusto C. Elliptic PDEs, measures and capacities: From the Poisson equation to nonlinear Thomas-Fermi problems. Zürich: European Mathematical Society, 2016.

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3

C.I.M.E. Summer School (2007 : Cetraro, Italy), ed. Geometric analysis and PDEs: Lectures given at the C.I.M.E. summer school held in Cetraro, Italy June 11-16, 2007. Berlin: Springer-Verlag, 2009.

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4

Hyperbolic partial differential equations and geometric optics. Providence, R.I: American Mathematical Society, 2012.

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5

Citti, Giovanna, Maria Manfredini, Daniele Morbidelli, Sergio Polidoro, and Francesco Uguzzoni, eds. Geometric Methods in PDE’s. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-02666-4.

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6

Geometric asymptotics for nonlinear PDE. Providence, R.I: American Mathematical Society, 2001.

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7

Prastaro, Agostino. Geometry of PDEs and mechanics. Singapore: World Scientific, 1996.

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8

Ferone, Vincenzo, Tatsuki Kawakami, Paolo Salani, and Futoshi Takahashi, eds. Geometric Properties for Parabolic and Elliptic PDE's. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-73363-6.

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9

Gazzola, Filippo, Kazuhiro Ishige, Carlo Nitsch, and Paolo Salani, eds. Geometric Properties for Parabolic and Elliptic PDE's. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-41538-3.

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10

Magnanini, Rolando, Shigeru Sakaguchi, and Angelo Alvino, eds. Geometric Properties for Parabolic and Elliptic PDE's. Milano: Springer Milan, 2013. http://dx.doi.org/10.1007/978-88-470-2841-8.

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11

Magnanini, Rolando. Geometric Properties for Parabolic and Elliptic PDE's. Milano: Springer Milan, 2013.

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12

Barbara, Opozda, Simon Udo 1938-, Wiehe Martin, and Stefan Banach International Mathematical Center., eds. PDEs, submanifolds and affine differential geometry. Warszawa: Polish Academy of Sciences, Institute of Mathematics, 2005.

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13

Martin, Wiehe, Simon Udo 1938-, Opozda Barbara, and Stefan Banach International Mathematical Center., eds. PDEs, submanifolds, and affine differential geometry. Warszawa: Polish Academy of Sciences, Institute of Mathematics, 2002.

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14

Wiehe, Martin. PDEs, submanifolds and affine differential geometry. Edited by Stefan Banach International Mathematical Center. Warszawa: Polish Academy of Sciences, Institute of Mathematics, 2005.

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15

Chanillo, Sagun, Paulo D. Cordaro, Nicholas Hanges, Jorge Hounie, and Abdelhamid Meziani, eds. Geometric Analysis of PDE and Several Complex Variables. Providence, Rhode Island: American Mathematical Society, 2005. http://dx.doi.org/10.1090/conm/368.

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16

Croke, Christopher B., Michael S. Vogelius, Gunther Uhlmann, and Irena Lasiecka, eds. Geometric Methods in Inverse Problems and PDE Control. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4684-9375-7.

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17

Croke, Christopher B. Geometric Methods in Inverse Problems and PDE Control. New York, NY: Springer New York, 2004.

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18

Druet, Olivier. Blow-up theory for elliptic PDEs in Riemannian geometry. Princeton, NJ: Princeton University Press, 2004.

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19

Olivier·, Druet·. Blow-up theory for elliptic PDEs in Riemannian geometry. Princeton· NJ: Princeton University Press·, 2003.

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20

Glimpses of soliton theory: The algebra and geometry of nonlinear PDEs. Providence, R.I: American Mathematical Society, 2010.

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21

1930-, Treves Francois, and Chanillo Sagun 1955-, eds. Geometric analysis of PDE and several complex variables: Dedicated to François Treves. Providence, R.I: American Mathematical Society, 2005.

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22

Shubin, M. A. Spectral theory and geometric analysis: An international conference in honor of Mikhail Shubin's 65th birthday, July 29 - August 2, 2009, Northeastern University, Boston, Massachusetts. Providence, R.I: American Mathematical Society, 2010.

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23

author, Tian Gang 1958, ed. The geometrization conjecture. Providence, Rhode Island: American Mathematical Society, 2014.

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24

Spaces of constant curvature. 6th ed. Providence, R.I: AMS Chelsea Pub., 2011.

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25

Houdre, Christian, and Christian Houdré. Concentration, functional inequalities, and isoperimetry: International workshop, October 29-November 1, 2009, Florida Atlantic University, Boca Raton, Florida. Providence, R.I: American Mathematical Society, 2011.

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26

Giancarlo, Benettin, Henrard J, Kuksin Sergej B. 1955-, Giorgilli Antonio, Centro internazionale matematico estivo, and European Mathematical Society, eds. Hamiltonian dynamics theory and applications: Lectures given at the C.I.M.E.-E.M.S. Summer School, held in Cetraro, Italy, July 1-10, 1999. Berlin: Springer, 2005.

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27

Schurz, Henri, Philip J. Feinsilver, Gregory Budzban, and Harry Randolph Hughes. Probability on algebraic and geometric structures: International research conference in honor of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea, June 5-7, 2014, Southern Illinois University, Carbondale, Illinois. Edited by Mohammed Salah-Eldin 1946- and Mukherjea Arunava 1941-. Providence, Rhode Island: American Mathematical Society, 2016.

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28

Semiclassical analysis. Providence, R.I: American Mathematical Society, 2012.

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29

Bonito, Andrea, and Ricardo H. Nochetto. Geometric PDEs. Elsevier Science & Technology, 2020.

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30

Geometric Properties For Parabolic And Elliptic Pdes. Springer Verlag, 2012.

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31

Uguzzoni, Francesco, Giovanna Citti, Maria Manfredini, Daniele Morbidelli, and Sergio Polidoro. Geometric Methods in PDE’s. Springer, 2015.

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32

Uguzzoni, Francesco, Giovanna Citti, Maria Manfredini, Daniele Morbidelli, and Sergio Polidoro. Geometric Methods in PDE's. Springer, 2015.

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33

Uguzzoni, Francesco, Giovanna Citti, Maria Manfredini, Daniele Morbidelli, and Sergio Polidoro. Geometric Methods in PDE’s. Springer, 2016.

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34

Sakaguchi, Shigeru, Rolando Magnanini, and Angelo Alvino. Geometric Properties for Parabolic and Elliptic PDE's. Springer Milan, 2014.

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35

Ferone, Vincenzo, Tatsuki Kawakami, Paolo Salani, and Futoshi Takahashi. Geometric Properties for Parabolic and Elliptic PDE's. Springer International Publishing AG, 2022.

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36

Ferone, Vincenzo, Tatsuki Kawakami, Paolo Salani, and Futoshi Takahashi. Geometric Properties for Parabolic and Elliptic PDE's. Springer International Publishing AG, 2021.

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37

Cabré, Xavier. Geometry of PDEs and Related Problems: Cetraro, Italy 2017. Springer, 2018.

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38

Rajeev, S. G. Fluid Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.001.0001.

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Abstract:

Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using conformal transformations, viscous flows such as Couette and Stokes flow around a sphere, shocks in the Burgers equation. Prandtl’s boundary layer theory and the Blasius solution are presented. Rayleigh–Taylor instability is studied in analogy with the inverted pendulum, with a digression on Kapitza’s stabilization. The possibility of transients in a linearly stable system with a non-normal operator is studied using an example by Trefethen et al. The integrable models (KdV, Hasimoto’s vortex soliton) and their hamiltonian formalism are studied. Delving into deeper mathematics, geodesics on Lie groups are studied: first using the Lie algebra and then using Milnor’s approach to the curvature of the Lie group. Arnold’s deep idea that Euler’s equations are the geodesic equations on the diffeomorphism group is then explained and its curvature calculated. The next three chapters are an introduction to numerical methods: spectral methods based on Chebychev functions for ODEs, their application by Orszag to solve the Orr–Sommerfeld equation, finite difference methods for elementary PDEs, the Magnus formula and its application to geometric integrators for ODEs. Two appendices give an introduction to dynamical systems: Arnold’s cat map, homoclinic points, Smale’s horse shoe, Hausdorff dimension of the invariant set, Aref ’s example of chaotic advection. The last appendix introduces renormalization: Ising model on a Cayley tree and Feigenbaum’s theory of period doubling.

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39

Buffa, Annalisa, and Giancarlo Sangalli. IsoGeometric Analysis : a New Paradigm in the Numerical Approximation of PDEs: Cetraro, Italy 2012. Springer London, Limited, 2016.

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40

Buffa, Annalisa, and Giancarlo Sangalli. IsoGeometric Analysis : A New Paradigm in the Numerical Approximation of PDEs: Cetraro, Italy 2012. Springer, 2017.

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41

Salani, Paolo, Filippo Gazzola, Kazuhiro Ishige, and Carlo Nitsch. Geometric Properties for Parabolic and Elliptic Pde's: Gppepdes, Palinuro, Italy, May 2015. Springer International Publishing AG, 2016.

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42

Salani, Paolo, Filippo Gazzola, Kazuhiro Ishige, and Carlo Nitsch. Geometric Properties for Parabolic and Elliptic PDE's: GPPEPDEs, Palinuro, Italy, May 2015. Springer London, Limited, 2016.

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43

Salani, Paolo, Filippo Gazzola, Kazuhiro Ishige, and Carlo Nitsch. Geometric Properties for Parabolic and Elliptic PDE's: GPPEPDEs, Palinuro, Italy, May 2015. Springer International Publishing AG, 2018.

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44

Lee, Dan A. Geometric Relativity. American Mathematical Society, 2019.

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45

Geometric Relativity. American Mathematical Society, 2019.

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46

(Editor), Christopher B. Croke, Gunther Uhlmann (Editor), Irena Lasiecka (Editor), and Michael S. Vogelius (Editor), eds. Geometric Methods in Inverse Problems and PDE Control (The IMA Volumes in Mathematics and its Applications). Springer, 2004.

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47

Adimurthi, K. Sandeep, Ian Schindler, and Cyril Tintarev. Concentration Analysis and Applications to PDE: ICTS Workshop, Bangalore, January 2012. Birkhäuser, 2013.

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48

Adimurthi, K. Sandeep, Ian Schindler, and Cyril Tintarev. Concentration Analysis and Applications to PDE: ICTS Workshop, Bangalore, January 2012. Birkhauser Verlag, 2013.

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49

Asymptotics In Dynamics Geometry And Pdes Generalized Borel Summation Proceedings Of The Conference Held In Crm Pisa 1216 October 2009 Vol Ii. Edizioni Della Normale, 2011.

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50

Foundations of Arithmetic Differential Geometry. American Mathematical Society, 2017.

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