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 is written by Victor Shapiro and published by CRC Press. It's available with International Standard Book Number or ISBN identification 1040197949 (ISBN 10) and 9781040197943 (ISBN 13).

Discussing many results and studies from the literature, this work illustrates the value of Fourier series methods in solving difficult nonlinear 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, presents the periodic Ca-theory of Calderon and Zygmund, and explores the extension of Fatou's famous work on antiderivatives and nontangential limits to higher dimensions. The importance of surface spherical harmonic functions is emphasized throughout.