Nonlinear Second Order Parabolic Equations

"The parabolic partial differential equations model is one of the most important processes in the process of diffusion in nature. Whether it is the diffusion of energy in space-time, the diffusion of species in ecology, the diffusion of chemicals in biochemical processes, or the diffusion of information in social networks, diffusion processes are ubiquitous and crucial in the physical and natural world as well as our everyday lives. In this graduate textbook, the author starts with classical parabolic problems as well as basic methods and techniques to guide students into the field of second order nonlinear parabolic equations. The author then moves on to discuss key topics such as theory and Schauder theory, the maximum principle and the comparison principle. Topics additionally discussed include periodic boundary value problems, free boundary problems, and semigroup theory. This book is based on tried and tested teaching materials used at the Harbin Institute of Technology over the past 10 years. Special care is taken to make the book suitable for classroom teaching as well as for self-study among graduate students"--