Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 30, pp. 1-9.

Title: A comparison principle for a class of subparabolic equations in
       Grushin-type spaces

Author: Thomas Bieske (Univ. of South Florida, Tampa, FL, USA)
 
Abstract:
 We define two notions of viscosity solutions to subparabolic
 equations in Grushin-type spaces, depending on whether the test
 functions concern only the past or both the past and the future.
 We then prove a comparison principle for a class of subparabolic
 equations and show the sufficiency of considering the test functions
 that concern only the past. 
  
Submitted November 27, 2006. Published February 14, 2007.
Math Subject Classifications: 35K55, 49L25, 53C17.
Key Words: Grushin-type spaces; parabolic equations; viscosity solutions.