On metric viscosity solutions for Hamilton-Jacobi equations of evolution   type
  This paper studies Hamilton-Jacobi equations of evolution type defined in a general metric space. We give a notion of a solution through optimal principles and establish a unique existence theorem of the solution for initial value problems. We also note a relationship between the notion of a solution and another notion based on characterization of the modulus of the gradient in the sense of [13]. 
Atsushi Nakayasu
math.AP