We consider a parabolic perturbation of the Hamilton-Jacobi equation where the potential is periodic in space and time. We show that any solution converges to a limit not depending on initial conditions.
@article{bwmeta1.element.bwnjournal-article-fmv157i2p299bwm, author = {Yakov Sinai}, title = {Parabolic perturbations of Hamilton--Jacobi equations}, journal = {Fundamenta Mathematicae}, volume = {158}, year = {1998}, pages = {299-303}, zbl = {0918.70010}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv157i2p299bwm} }
Sinai, Yakov. Parabolic perturbations of Hamilton–Jacobi equations. Fundamenta Mathematicae, Tome 158 (1998) pp. 299-303. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv157i2p299bwm/
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