# Gradient bounds for nonlinear degenerate parabolic equations and application to large time behavior of systems

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Abstract : We obtain new oscillation and gradient bounds for the viscosity solutions of fully nonlinear degenerate elliptic equations where the Hamiltonian is a sum of a sublinear and a superlinear part in the sense of Barles and Souganidis (2001). We use these bounds to study the asymptotic behavior of weakly coupled systems of fully nonlinear parabolic equations. Our results apply to some asymmetric systems'' where some equations contain a sublinear Hamiltonian whereas the others contain a superlinear one. Moreover, we can deal with some particular case of systems containing some degenerate equations using a generalization of the strong maximum principle for systems.
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Journal articles

https://hal.archives-ouvertes.fr/hal-01022962
Contributor : Olivier Ley <>
Submitted on : Friday, May 15, 2015 - 10:31:16 AM
Last modification on : Thursday, November 15, 2018 - 11:57:45 AM
Long-term archiving on : Tuesday, September 15, 2015 - 12:42:03 AM

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### Citation

Olivier Ley, Vinh Duc Nguyen. Gradient bounds for nonlinear degenerate parabolic equations and application to large time behavior of systems. Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2016, 130, pp.76-101. ⟨10.1016/j.na.2015.09.012⟩. ⟨hal-01022962v2⟩

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