Basic Guide to Uniqueness Problems for Evolutionary Differential Equations

This book addresses the issue of uniqueness of a solution to a problem – a very important topic in science and technology, particularly in the field of partial differential equations, where uniqueness guarantees that certain partial differential equations are sufficient to model a given phenomenon. 

The reader is expected to learn various fundamental ideas and techniques in mathematical analysis for partial differential equations by establishing uniqueness. No prerequisite other than simple calculus and linear algebra is necessary. For the reader’s convenience, a list of basic terminology is given at the end of this book.

Dr. Yoshikazu Giga is professor at the Graduate School of Mathematical Sciences of the University of Tokyo, Japan. He is a fellow of the American Mathematical Society as well as of the Japan Society for Industrial and Applied Mathematics. Through his more than 250 papers and 2 monographs, he has substantially contributed to the theory for parabolic partial differential equations including geometric evolution equations, semilinear heat equations, as well as the incompressible Navier-Stokes equations. He has received several prizes including the Medal of Honor with Purple Ribbon from the Government of Japan and the second Kodaira Kunihiko Prize from the Mathematical Society of Japan.

Dr. Mi-Ho Giga is a project researcher at the Graduate School of Mathematical Sciences of the University of Tokyo, Japan. She is a mathematical analyst working on parabolic partial differential equations related to crystal growth at low temperature. She is a member of both the Mathematical Society of Japan and the Japan Society for Industrial and Applied Mathematics. She is one of the authors of the book 'Nonlinear Partial Differential Equations: Asymptotic Behavior of Solutions and Self-Similar Solutions' published from Birkhauser in 2010 as well as its Japanese original version published from Kyoritu-Shuppan in 1999.