# Partial Differential Equations: Theory, Numerical Methods and Ill-Posed Problems

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Michael V. Klibanov (Author) – Professor, Department of Mathematics and Statistics, University of North Carolina, Charlotte, NC, USA
Jingzhi Li (Author) – Professor, Department of Mathematics, Southern University of Science and Technology, Shenzhen, China

Series: Mathematics Research Developments
BISAC: MAT007020
DOI: https://doi.org/10.52305/TTIO3667

The laws of nature are written in the language of partial differential equations. Therefore, these equations arise as models in virtually all branches of science and technology. Our goal in this book is to help you to understand what this vast subject is about. The book is an introduction to the field suitable for senior undergraduate and junior graduate students.

Introductory courses in partial differential equations (PDEs) are given all over the world in various forms. The traditional approach to the subject is to introduce a number of analytical techniques, enabling the student to derive exact solutions of some simplified problems. Students who learn about computational techniques in other courses subsequently realize the scope of partial differential equations beyond paper and pencil.

Our book is significantly different from the existing ones. We introduce both analytical theory, including the theory of classical solutions and that of weak solutions, and introductory techniques of ill-posed problems with reference to weak solutions. Besides, since computational techniques are commonly available and are currently used in all practical applications of partial differential equations, we incorporate classical finite difference methods and finite element methods in our book.

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ISBN: N/A

Preface

Acknowledgments

Chapter 1. Introduction

Chapter 2. Analytic Approaches to Linear PDEs

Chapter 3. Transformation Approaches to Certain PDEs

Chapter 4. Function Spaces

Chapter 5. Elliptic PDEs

Chapter 6. Hyperbolic PDEs

Chapter 7. Parabolic PDEs

Chapter 8. Introduction to Ill-posed Problems

Chapter 9. Finite Difference Method

Chapter 10. Finite Element Method

Chapter 11. Conclusion

Index