Fourier Series in Several Variables with Applications to Partial Differential Equations (Chapman & Hall/Crc Applied Mathematics and Nonlinear Science Series) - Hardcover

Shapiro, Victor L.

 
9781439854273: Fourier Series in Several Variables with Applications to Partial Differential Equations (Chapman & Hall/Crc Applied Mathematics and Nonlinear Science Series)
Hardcover
ISBN 10: 1439854270 ISBN 13: 9781439854273
Verlag: Chapman and Hall/CRC, 2019

Inhaltsangabe

Fourier Series in Several Variables with Applications to Partial Differential Equations illustrates the value of Fourier series methods in solving difficult nonlinear partial differential equations (PDEs). Using these methods, the author presents results for stationary Navier-Stokes equations, nonlinear reaction-diffusion systems, and quasilinear elliptic PDEs and resonance theory. He also establishes the connection between multiple Fourier series and number theory.





The book first presents four summability methods used in studying multiple Fourier series: iterated Fejer, Bochner-Riesz, Abel, and Gauss-Weierstrass. It then covers conjugate multiple Fourier series, the analogue of Cantor’s uniqueness theorem in two dimensions, surface spherical harmonics, and Schoenberg’s theorem. After describing five theorems on periodic solutions of nonlinear PDEs, the text concludes with solutions of stationary Navier-Stokes equations.





Discussing many results and studies from the literature, this book demonstrates the robust power of Fourier analysis in solving seemingly impenetrable nonlinear problems.

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Über die Autorin bzw. den Autor

Victor L. Shapiro is a Distinguished Professor Emeritus in the Department of Mathematics at the University of California, Riverside, where he has taught for 46 years. He earned his Ph.D. from the University of Chicago and completed postdoctoral work at the Institute for Advanced Study, where he was an NSF fellow.

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Verlag
Chapman and Hall/CRC
Erscheinungsdatum
2019
Sprache
Englisch
ISBN 10 
1439854270
ISBN 13 
9781439854273
Einband
Gebundene Ausgabe
Anzahl der Seiten
338
Kontakt zum Hersteller
CRC Press
https://www.routledge-ny.com

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Weitere beliebte Ausgaben desselben Titels

9780367382926: Fourier Series in Several Variables with Applications to Partial Differential Equations (Chapman & Hall/Crc Applied Mathematics and Nonlinear Science)

Vorgestellte Ausgabe

ISBN 10:  036738292X ISBN 13:  9780367382926
Verlag: Routledge, 2019
Softcover