We define two notions of viscosity solutions to parabolic equations defined using vector fields, depending on whether the test functions concern only the past or both the past and the future. Using the parabolic maximum principle for vector fields, we then prove a comparison principle for a class of parabolic equations and show the sufficiency of considering the test functions that concern only the past.
Submitted July 7, 2008. Published September 4, 2008.
Math Subject Classifications: 35K55, 49L25, 35H20.
Key Words: Viscosity solutions; vector fields; parabolic equations.
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| Thomas Bieske |
Department of Mathematics, University of South Florida
Tampa, FL 33620, USA
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