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Large Time Behavior of Periodic Viscosity Solutions for Uniformly Parabolic Integro-Differential Equations
Abstract : In this paper, we study the large time behavior of solutions of a class of parabolic fully nonlinear integro-differential equations in a periodic setting. In order to do so, we first solve the ergodic problem}(or cell problem), i.e. we construct solutions of the form $\lambda t + v(x)$. We then prove that solutions of the Cauchy problem look like those specific solutions as time goes to infinity. We face two key difficulties to carry out this classical program: (i) the fact that we handle the case of ''mixed operators'' for which the required ellipticity comes from a combination of the properties of the local and nonlocal terms and (ii) the treatment of the superlinear case (in the gradient variable). Lipschitz estimates previously proved by the authors (2012) and Strong Maximum principles proved by the third author (2012) play a crucial role in the analysis.
Cited literature [40 references]
https://hal.archives-ouvertes.fr/hal-00743751
Contributor : Adina Ciomaga Connect in order to contact the contributor
Submitted on : Friday, October 19, 2012 - 10:24:51 PM
Last modification on : Saturday, January 15, 2022 - 4:13:42 AM
Long-term archiving on: : Sunday, January 20, 2013 - 3:40:30 AM
Contributor : Adina Ciomaga Connect in order to contact the contributor
Submitted on : Friday, October 19, 2012 - 10:24:51 PM
Last modification on : Saturday, January 15, 2022 - 4:13:42 AM
Long-term archiving on: : Sunday, January 20, 2013 - 3:40:30 AM
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