Linear and semilinear partial differential equations : an introduction / Radu Precup.

Format:

Book

Author/Creator:

Precup, Radu.

Series:

De Gruyter Textbook

De Gruyter textbook

Language:

English

Subjects (All):

Differential equations, Linear--Textbooks.

Differential equations, Linear.

Differential equations, Partial--Textbooks.

Differential equations, Partial.

Physical Description:

1 online resource (296 p.)

Edition:

1st ed.

Place of Publication:

Berlin : Radu Precup De Gruyter, [2013]

Language Note:

English

Summary:

The text is intended for students who wish a concise and rapid introduction to some main topics in PDEs, necessary for understanding current research, especially in nonlinear PDEs. Organized on three parts, the book guides the reader from fundamental classical results, to some aspects of the modern theory and furthermore, to some techniques of nonlinear analysis. Compared to other introductory books in PDEs, this work clearly explains the transition from classical to generalized solutions and the natural way in which Sobolev spaces appear as completions of spaces of continuously differentiable functions with respect to energetic norms. Also, special attention is paid to the investigation of the solution operators associated to elliptic, parabolic and hyperbolic non-homogeneous equations anticipating the operator approach of nonlinear boundary value problems. Thus the reader is made to understand the role of linear theory for the analysis of nonlinear problems.

Contents:

Front matter

Preface

Notation

Contents

Part I. Classical Theory

Chapter 1. Preliminaries

Chapter 2. Partial Differential Equations and Mathematical Modeling

Chapter 3. Elliptic Boundary Value Problems

Chapter 4. Mixed Problems for Evolution Equations

Chapter 5. The Cauchy Problem for Evolution Equations

Part II. Modern Theory

Chapter 6. Distributions

Chapter 7. Sobolev Spaces

Chapter 8. The Variational Theory of Elliptic Boundary Value Problems

Part III. Semilinear Equations

Chapter 9. Semilinear Elliptic Problems

Chapter 10. The Semilinear Heat Equation

Chapter 11. The Semilinear Wave Equation

Chapter 12 Semilinear Schrödinger Equations

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9783110269055

3110269058

OCLC:

828137762