ENGLISH

Partial Differential Equations in Sobolev and Analytic Spaces

By Svetlin G. Georgiev , Khaled Zennir , Aissa Boukarou

Book information

Publisher
World Scientific
Year
2025
ISBN
9789811298509, 9789811298516, 9789811298523
DOI
10.1142/13994
Language
english
Format
PDF
Filesize
10 MB (10781677 bytes)
Edition
1
Pages
632\633
Orientation
yes
Paginated
no
Scanned
portrait
Time added
2025-02-05 16:43:48
Analytic SpacesDistributionsFourier TransformKadomtsev–Petviashvili EquationKdV EquationNonlinear Dispersive EquationsShallow Water EquationSobolev spaces

Description

Partial Differential Equations (PDEs) are fundamental in fields such as physics and engineering, underpinning our understanding of sound, heat, diffusion, electrostatics, electrodynamics, thermodynamics, fluid dynamics, elasticity, general relativity, and quantum mechanics. They also arise in areas like differential geometry and the calculus of variations. This book focuses on recent investigations of PDEs in Sobolev and analytic spaces. It consists of twelve chapters, starting with foundational definitions and results on linear, metric, normed, and Banach spaces, which are essential for introducing weak solutions to PDEs. Subsequent chapters cover topics such as Lebesgue integration, Lp spaces, distributions, Fourier transforms, Sobolev and Bourgain spaces, and various types of KdV equations. Advanced topics include higher order dispersive equations, local and global well-posedness, and specific classes of Kadomtsev-Petviashvili equations. This book is intended for specialists like mathematicians, physicists, engineers, and biologists. It can serve as a graduate-level textbook and a reference for multiple disciplines.

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