Basic Guide to Uniqueness Problems for Evolutionary Differential Equations

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.

• 1 Uniqueness of solutions to initial value problems for ordinary differential equation.- 2 Ordinary differential equations and transport equation.- 3 Uniqueness of solutions to initial value problems for a scalar conversation law.- 4 Hamilton-Jacobi equations.- 5 Appendix: Basic terminology.