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Article overview
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Large time behavior of solutions to a degenerate parabolic Hamilton-Jacobi-Bellman equation | | Daniele Castorina
; Annalisa Cesaroni
; Luca Rossi
; | | Date: |
1 Sep 2015 | | Abstract: | We derive the long time asymptotic of solutions to an evolutive
Hamilton-Jacobi-Bellman equation in a bounded smooth domain, in connection with
ergodic problems recently studied in [1]. Our main assumption is an appropriate
degeneracy condition on the operator at the boundary. This condition is related
to the characteristic boundary points for linear operators as well as to the
irrelevant points for the generalized Dirichlet problem, and implies in
particular that no boundary datum has to be imposed. We prove that there exists
a constant c such that the solutions of the evolutive problem converge
uniformly, in the reference frame moving with constant velocity c, to a unique
steady state solving a suitable ergodic problem. | | Source: | arXiv, 1509.0177 | | Services: | Forum | Review | PDF | Favorites | |
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