Nonlinear Second Order Parabolic Equations

The parabolic partial differential equations model diffusion, which is essential in the physical and natural world and our everyday lives. This book covers key topics such as the Lp theory and Schauder theory, maximum principle, comparison principle, regularity and uniform estimates, initial-boundary value problems, upper and lower solutions method, monotone properties, long-time behaviors, convergence of solutions, stability of equilibrium solutions, global solutions, and finite time blowup. It is based on teaching materials used at the Harbin Institute of Technology and is suitable for classroom teaching and self-study.

Format: Hardback
Length: 288 pages
Publication date: 13 May 2021
Publisher: Taylor & Francis Ltd

Diffusion is a fundamental process that plays a crucial role in various real-world phenomena, ranging from the spread of energy in space-time to the movement of species in ecology, the diffusion of chemicals in biochemical reactions, and the dissemination of information in social networks. Understanding the dynamics of diffusion is essential for predicting and analyzing complex systems, and this book aims to provide a comprehensive and accessible introduction to the field.

The book is self-contained and covers a wide range of topics, including the Lp theory and Schauder theory, the maximum principle, the comparison principle, regularity and uniform estimates, initial-boundary value problems of semilinear parabolic scalar equations and weakly coupled parabolic systems, the upper and lower solutions method, monotone properties and long-time behaviors of solutions, convergence of solutions and stability of equilibrium solutions, global solutions and finite time blowup. It also touches on periodic boundary value problems, free boundary problems, and semigroup theory.

One of the key features of the book is its emphasis on practical applications. It includes numerous examples and exercises that illustrate the theoretical concepts and help students apply them to real-world problems. The book is designed to be suitable for classroom teaching as well as for self-study among graduate students.

The author, Mingxin Wang, is a Professor of Mathematics at the Harbin Institute of Technology, China. He has published ten monographs and textbooks and has authored over 260 papers. He has extensive experience in teaching and has supervised numerous PhD students.

In conclusion, this book is a valuable resource for anyone interested in learning about the theory and applications of parabolic partial differential equations. It provides a comprehensive and accessible introduction to the field, covering key topics and emphasizing practical applications. Whether you are a student, researcher, or professional in the field, this book will help you deepen your understanding of diffusion and its role in the physical and natural world.

Weight: 734g
Dimension: 182 x 263 x 24 (mm)
ISBN-13: 9780367711986