Electron. J. Diff. Eqns.,
Vol. 2008(2008), No. 124, pp. 17.
Parabolic equations relative to vector fields
Thomas Bieske
Abstract:
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
email: tbieske@math.usf.edu

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