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- Fourier Analysis and Nonlinear Partial Differential Equations
- Fourier Analysis and Nonlinear Partial Differential Equations

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Part of the Grundlehren der mathematischen Wissenschaften book series GL, volume In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations. It also offers more sophisticated models originating from fluid mechanics in particular the incompressible and compressible Navier-Stokes equations or general relativity. It is either directed to anyone with a good undergraduate level of knowledge in analysis or useful for experts who are eager to know the benefit that one might gain from Fourier analysis when dealing with nonlinear partial differential equations.

The corrected Fourier series CFS is proposed for solving partial differential equations PDEs with fractional time derivative on a finite domain. In the previous work, we have been solving partial differential equations by using corrected Fourier series. The fractional derivatives are described in Riemann sense. Some numerical examples are presented to show the solutions. In recent years, differential equations of fractional orders have been appearing more and more frequently in various research and applications in the fluid mechanics, viscoelasticity, biology, physics, and engineering; see [ 1 , 2 ]. There are some methods usually used in solving the fractional partial differential equations such as Laplace and Fourier transform, variational iteration method, and differential transform methods.

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Bahouri and J. Chemin and R. Bahouri , J. Chemin , R.

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Part of the Grundlehren der mathematischen Wissenschaften book series GL, volume In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations.

*It seems that you're in Germany. We have a dedicated site for Germany. In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations.*

There are two sections, one of five chapters on classical theory of the mechanics of continua based on Hamilton's principle and another of four chapters on partial differential equations. The author does show his usual clarity and elegance and the. Professor Copson is distinguished for his work on Analysis , particularly on partial differential equations , and has written a number of excellent textbooks.

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## Nadine F.

Fourier Analysis and Nonlinear Partial Differential Equations. Authors; (view Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin. Pages PDF.