عنوان

Dispersive Partial Differential Equations.

(Number (ISBN

131656326X

(Number (ISBN

9781316563267

Number

b391563

Title Proper

Dispersive Partial Differential Equations.

General Material Designation

[Book]

Place of Publication, Distribution, etc.

Cambridge

Name of Publisher, Distributor, etc.

Cambridge University Press,

Date of Publication, Distribution, etc.

2016.

Specific Material Designation and Extent of Item

(204 pages)

Text of Note

Cover Half-title Title page Copyright information Dedication Table of contents Preface Notation 1 Preliminaries and tools Exercises 2 Linear dispersive equations 2.1 Estimates on the real line 2.2 Estimates on the torus 2.3 The Talbot effect Exercises 3 Methods for establishing wellposedness 3.1 The energy method 3.1.1 A priori bounds 3.1.2 Existence and uniqueness 3.1.3 Growth bounds for KdV with potential 3.2 Oscillatory integral method 3.3 Restricted norm method 3.3.1 L[sup(2)] solutions of KdV on the real line 3.3.2 Low regularity solutions of KdV on the torus. 3.3.3 Forced and damped KdV with a potential3.4 Differentiation by parts on the torus: unconditional wellposedness 3.5 Local theory for NLS on the torus 3.5.1 L[sup(2)] wellposedness of cubic NLS on the torus 3.5.2 H[sup(s)] local wellposedness of the quintic NLS on the torus 3.6 Illposedness results Exercises 4 Global dynamics of nonlinear dispersive PDEs 4.1 Smoothing for nonlinear dispersive PDEs on the torus 4.1.1 Cubic NLS on the torus 4.1.2 The KdV equation on the torus 4.1.3 Proof of Proposition 4.7 4.2 High-low decomposition method. 4.3 The I-method for the quintic NLS equation on the torusExercises 5 Applications of smoothing estimates 5.1 Bounds for higher order Sobolev norms 5.2 Almost everywhere convergence to initial data 5.3 Nonlinear Talbot effect 5.4 Global attractors for dissipative and dispersive PDEs 5.4.1 The global attractor is trivial for large damping 5.4.2 Bounds on the forced KdV equation Exercises References Index.

Text of Note

Provides a self-contained and accessible introduction to nonlinear dispersive partial differential equations (PDEs) for graduate or advanced undergraduate students in mathematics, engineering, andProvides a self-contained and accessible introduction to nonlinear dispersive partial differential equations (PDEs) for graduate or advanced undergraduate students in mathematics, engineering, andProvides a self-contained and accessible introduction to nonlinear dispersive partial differential equations (PDEs) for graduate or advanced undergraduate students in mathematics, engineering, and

Electronic books

M Burak Erdoğan

Nikolaos Tzirakis

Electronic name

[Book]

Y