Electron. J. Diff. Eqns., Vol. 2007(2007), No. 30, pp. 1-9.

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

Thomas Bieske

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.

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Thomas Bieske
Department of Mathematics
University of South Florida
Tampa, FL 33620, USA
email: tbieske@math.usf.edu

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