Zobrazeno 1 - 10
of 10
pro vyhledávání: '"Junyilang Zhao"'
Autor:
Jun Shen, Junyilang Zhao
Publikováno v:
Journal of Differential Equations. 303:86-122
We study long time dynamics of a randomly perturbed non-autonomous coupled system ( x , y ) , whose x coordinate satisfies a semilinear parabolic equation with an additive noise, and y coordinate satisfies a differential equation whose solutions do n
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::009d790a038f0e27554cccbe3bee7b25
https://doi.org/10.1016/j.jde.2021.09.018
https://doi.org/10.1016/j.jde.2021.09.018
Publikováno v:
Journal of Differential Equations. 269:5997-6054
In this paper, we prove that for a random differential equation with the driving noise constructed from a Q-Wiener process and the Wiener shift, there exists a local center, unstable, stable, center-unstable, center-stable manifold, and a local stabl
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fb15f771048a08413ebb9567e84466f3
https://doi.org/10.1016/j.jde.2020.04.032
https://doi.org/10.1016/j.jde.2020.04.032
Publikováno v:
Stochastic Analysis and Applications. 38:1019-1044
This paper deals with the limiting behavior of non-autonomous stochastic reaction-diffusion equations without uniqueness on unbounded narrow domains. We prove the existence and upper semicontinuity...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ab5b286df1d3637a59f857957d5d4628
https://doi.org/10.1080/07362994.2020.1755311
https://doi.org/10.1080/07362994.2020.1755311
Publikováno v:
Communications on Pure & Applied Analysis. 19:2751-2776
In this paper, we study the long term behavior of non-autonomous fractional FitzHugh-Nagumo systems with random forcing given by an approximation of white noise, called Wong-Zakai approximation. We first prove the existence and uniqueness of tempered
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::845e4eed12a9ad3493f3dffc029cc031
https://doi.org/10.3934/cpaa.2020120
https://doi.org/10.3934/cpaa.2020120
Publikováno v:
Journal of Dynamics and Differential Equations.
In this paper, we study a class of semilinear parabolic equation and its perturbed system driven by a random force. Such driving noise is assumed to be a regular approximation to the white noise and satisfy certain properties. We show that the $$C^1$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::62c38b0ed75f73fd02801d29a7a6e6da
https://doi.org/10.1007/s10884-021-10103-4
https://doi.org/10.1007/s10884-021-10103-4
Autor:
Jun Shen, Junyilang Zhao
Publikováno v:
Proceedings of the American Mathematical Society. 148:365-377
In this paper, we give a new and quick proof for the Hartman-Grobman theorem for random dynamical systems. This approach does not involve any previously proved existence of the stable and unstable manifolds.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::da78bb9f0aa9479701b66e48b3a5095a
https://doi.org/10.1090/proc/14707
https://doi.org/10.1090/proc/14707
Publikováno v:
Journal of Differential Equations. 266:4568-4623
In this paper, we study the Wong–Zakai approximations given by a stationary process via the Wiener shift and their associated dynamics of a class of stochastic evolution equations with a multiplicative white noise. We prove that the solutions of Wo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7cd6d8c7d90afa942b558d12316f5a66
https://doi.org/10.1016/j.jde.2018.10.008
https://doi.org/10.1016/j.jde.2018.10.008
Publikováno v:
Journal of Mathematical Analysis and Applications. 506:125668
A class of retarded semilinear parabolic equation driven by an additive Q -Wiener process is studied. We construct a process via the Wiener shift to provide stationary approximations of the noise, and show that solutions of stationary approximations
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c1a27acdf5254132f68f51597dc4dd9d
https://doi.org/10.1016/j.jmaa.2021.125668
https://doi.org/10.1016/j.jmaa.2021.125668
Publikováno v:
Journal of Mathematical Physics. 61:112702
This paper deals with the limiting dynamical behavior of non-autonomous stochastic reaction–diffusion equations with time-varying delays on thin domains. First, we prove the existence and uniqueness of the regular random attractor. Then, we prove t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5df6e6d24b1f3982f613b2baaebf2697
https://doi.org/10.1063/5.0010398
https://doi.org/10.1063/5.0010398
Publikováno v:
Journal of Mathematical Physics; Nov2020, Vol. 61 Issue 11, p112702-1-112702-23, 23p