Fourier series in several variables with applications to partial differential equations - Shapiro, Victor L. (Victor Lenard), 1924-2013 (Chapman & Hall/CRC applied mathematics and nonlinear science series., 2011)
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, a.