Franklin

Linear and semilinear partial differential equations [electronic resource] : an introduction / Radu Precup.

Author/Creator:
Precup, Radu.
Publication:
Berlin : Radu Precup De Gruyter, [2013]
Format/Description:
Book
1 online resource (296 p.)
Series:
De Gruyter Textbook
De Gruyter textbook
De Gruyter Textbook
Status/Location:
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Details

Subjects:
Differential equations, Linear -- Textbooks.
Differential equations, Partial -- Textbooks.
Form/Genre:
Electronic books.
Language:
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:
3-11-026905-8
OCLC:
828137762
Publisher Number:
10.1515/9783110269055 doi