Geodesic
Gradient estimates for a nonlinear parabolic equation with potential under geometric flow
Electronic Journal of Differential Equations, Tome 2015 (2015).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let (M,g) be an n dimensional complete Riemannian manifold. In this article we prove local Li-Yau type gradient estimates for all positive solutions to the nonlinear parabolic equation $$ (\partial_t - \Delta_g + \mathcal{R}) u( x, t) = - a u( x, t) \log u( x, t) $$ along the generalised geometric flow on M. Here $\mathcal{R} = \mathcal{R} (x, t)$ is a smooth potential function and a is an arbitrary constant. As an application we derive a global estimate and a space-time Harnack inequality.
Classification : 35K55, 53C21, 53C44, 58J35
Keywords: gradient estimates, Harnack inequalities, parabolic equations, geometric flows 
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     author = {Abolarinwa, Abimbola},
     title = {Gradient estimates for a nonlinear parabolic equation with potential under geometric flow},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a19/}
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Abolarinwa, Abimbola. Gradient estimates for a nonlinear parabolic equation with potential under geometric flow. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a19/