Comportement en temps long des solutions de quelques équations de Hamilton-Jacobi du premier et second ordre, locales et non-locales, dans des cas non-périodiques

Abstract : The main aim of this thesis is to study large time behavior of unbounded solutions of viscous Hamilton-Jacobi equations in RN in presence of an Ornstein-Uhlenbeck drift. We also consider the same issue for a first order Hamilton-Jacobi equation. In the first case, which is the core of the thesis, we generalize the results obtained by Fujita, Ishii and Loreti (2006) in several directions. The first one is to consider more general operators. We first replace the Laplacian by a general diffusion matrix and then consider a non-local integro-differential operator of fractional Laplacian type. The second kind of extension is to deal with more general Hamiltonians which are merely sublinear.
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Thi Tuyen Nguyen. Comportement en temps long des solutions de quelques équations de Hamilton-Jacobi du premier et second ordre, locales et non-locales, dans des cas non-périodiques. Equations aux dérivées partielles [math.AP]. Université Rennes 1, 2016. Français. ⟨NNT : 2016REN1S089⟩. ⟨tel-01444956v2⟩

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