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Series : Graduate Studies in Mathematics

Partial Differential Equations, Ed. 2

¥ 8,834 (tax included)

Description

This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE. For this edition, the author has made numerous changes, including

a new chapter on nonlinear wave equations,
more than 80 new exercises,
several new sections,
a significantly expanded bibliography.

Contents

1. Introduction

PART I: REPRESENTATION FORMULAS FOR SOLUTIONS
2. Four Important Linear PDE
3. Nonlinear First-Order PDE
4. Other Ways to Represent Solutions

PART II: THEORY FOR LINEAR PARTIAL DIFFERENTIAL EQUATIONS
5. Sobolev Spaces
6. Second-Order Elliptic Equations
7. Linear Evolution Equations

PART III: THEORY FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
8. The Calculus of Variations
9. Nonvariational Techniques
10. Hamilton Jacobi Equations
11. Systems of Conservation Laws
12. Nonlinear Wave Equations

APPENDICES
Appendix A: Notation
Appendix B: Inequalities
Appendix C: Calculus
Appendix D: Functional Analysis
Appendix E: Measure Theory
Bibliography
Index