Название: Partial Differential Equations in Sobolev and Analytic SpacesАвтор: Aissa Boukarou, Khaled Zennir, Svetlin G Georgiev
Издательство: World Scientific
Год выхода: 2025
Страниц: 632
Формат: True PDF
Размер: 12,5 MB
Язык: английский
This book is devoted on some recent investigations of some classes partial differential equations in Sobolev and analytic spaces. The book contains twelve chapters. Chapter 1 is entirely devoted to the presentation of definitions and results necessary as a result of this work. We first recall a few basic results on the linear, metric, normed and Banach Spaces and its properties. These are used in particular to introduce the different concepts of weak solutions to PDEs.
Chapter 2 is titled ”Lebesgue Integration”, it is devoted to the study of measure and integration, Lebesgue measurable functions and general measure spaces, where there are many proved results. The purpose of Chapter 3 is to present results according to the Lp spaces, which contains definitions, separability, duality and general Lp spaces with its norms. Elements of theory of distributions are introduced in Chapter 4. It is introduced the Fourier transform in the spaces S and S0 and they are deducted some important properties. Sobolev spaces and Bourgain spaces are discussed in Chapter 5.
Chapter 6 is devoted on the original method for KdV equations in Sobolev spaces. In Chapter 7 are investigated some fifth order shallow water equations for local and global well posedness. Higher order dispersive equations are studied in Chapter 8. They are given criteria for existence of local global solutions in some analytic spaces. In Chapter 9 are investigated some classes fifth order Kadomtsev-Petviashvili I equations in Bourgain spaces for existence of solutions, continuous dependence on initial data and Gevrey regularity in t. They are studied some classes KadomtsevPetviashvili II equations in anisotropic Gevrey spaces. Chapter 10 is devoted on the generalized Kadomtsev-Petviashvili I equation. Coupled systems of KdV equations are introduced and studied in Chapter 11. In Chapter 12 are discussed coupled systems of generalized KdV equations