Linear and Semilinear Partial Differential Equations: An Introduction by Radu Pr

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Linear and Semilinear Partial Differential Equations

FORMATHardcover LANGUAGEEnglish CONDITIONBrand New Publisher Description

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.

Author Biography

Radu Precup, Babe?-Bolyai University of Cluj-Napoca, Romania.

Table of Contents

PART I: Classical Theory 1 Preliminaries; 2 Partial differential equations and mathematical modeling; 3 Elliptic boundary value problems; 4 Mixed problems for evolution equations; 5 The Cauchy problem for evolution equations; PART II: Modern Theory 6 Distributions; 7 Sobolev spaces; 8 Variational theory of elliptic boundary value problems; PART III: Semi-linear Equations 9 Semi-linear elliptic problems; 10 Semi-linear heat equation; 11 Semi-linear wave equation; 12 Nonlinear Schrodinger equations.

Long Description

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.

Details ISBN311026904X Author Radu Precup Language English ISBN-10 311026904X ISBN-13 9783110269048 Subtitle An Introduction Short Title LINEAR & SEMILINEAR PARTIAL DI Audience Age 18-21 Media Book Year 2012 Publication Date 2012-11-15 Place of Publication Berlin Country of Publication Germany Pages 296 Imprint De Gruyter Publisher De Gruyter Series De Gruyter Textbook Format Hardcover Alternative 9783110269055 DEWEY 515.354 Audience Tertiary & Higher Education We've got this

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