Fourier Series in Several Variables with Applications to Partial Differential Equations
Fourier Series in Several Variables with Applications to Partial Differential Equations
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Fourier Series in Several Variables with Applications to Partial Differential Equations by Victor Shapiro
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.
I found the book interesting.. Certainly, all readers and even the experts will find something new and relevant in it. -Atanas G. Stefanov, Mathematical Reviews, Issue 2012a
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.
| SKU | Unavailable |
| ISBN 13 | 9781439854273 |
| ISBN 10 | 1439854270 |
| Title | Fourier Series in Several Variables with Applications to Partial Differential Equations |
| Author | Victor Shapiro |
| Condition | Unavailable |
| Binding type | Hardback |
| Publisher | Taylor & Francis Inc |
| Year published | 2011-03-28 |
| Number of pages | 352 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |