Geodesic
Parabolic equations relative to vector fields
Electronic journal of differential equations, Tome 2008 (2008)
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.
Classification : 35K55, 49L25, 35H20
Keywords: viscosity solutions, vector fields, parabolic equations 
@article{EJDE_2008__2008__a88,
     author = {Bieske,  Thomas},
     title = {Parabolic equations relative to vector fields},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1173.35526},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a88/}
}
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%T Parabolic equations relative to vector fields
%J Electronic journal of differential equations
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Bieske,  Thomas. Parabolic equations relative to vector fields. Electronic journal of differential equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a88/