Author
Rongrong Tian
Other affiliations: Huazhong University of Science and Technology
Bio: Rongrong Tian is an academic researcher from Wuhan University of Technology. The author has contributed to research in topics: Uniqueness & Stochastic differential equation. The author has an hindex of 3, co-authored 10 publications receiving 26 citations. Previous affiliations of Rongrong Tian include Huazhong University of Science and Technology.
Papers
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TL;DR: In this article, the existence and uniqueness of weak Lp-solutions under the assumption that the coefficients are only in Sobolev spaces is established. And the non-negative weak lp-Solutions and renormalized solutions are derived.
Abstract: In this paper, we study the fractional Fokker-Planck equation and obtain the existence and uniqueness of weak Lp-solutions (1 ⩽ p ⩽ ∞) under the assumptions that the coefficients are only in Sobolev spaces. Moreover, to L∞-solutions, we gain the well-posedness for BV coefficients. Besides, the non-negative weak Lp-solutions and renormalized solutions are derived. After then, we achieve the stability for stationary solutions.
13 citations
TL;DR: In this article, the Lipschitz and W2 estimates for second-order parabolic PDE ∂tu(t,x) = 12Δu( t,x)+f(t,x) on Rd with zero initial data and f satisfying a Ladyzhenskaya-Prod...
Abstract: The goal of this paper is to establish the Lipschitz and W2,∞ estimates for a second-order parabolic PDE ∂tu(t,x)=12Δu(t,x)+f(t,x) on Rd with zero initial data and f satisfying a Ladyzhenskaya–Prod...
8 citations
TL;DR: A new scheme of parabolic approximation motivated by the method of vanishing viscosity given by Feng and Nualart is developed and it is proved the continuous dependence of stochastic strong entropy solutions on the coefficient b and the nonlinear function f.
Abstract: This paper considers the existence and uniqueness of stochastic entropy solution for a nonlinear transport equation with a stochastic perturbation. The uniqueness is based on the doubling variable method. For the existence, we develop a new scheme of parabolic approximation motivated by the method of vanishing viscosity given by Feng and Nualart (J. Funct. Anal. 2008, 255, 313–373). Furthermore, we prove the continuous dependence of stochastic strong entropy solutions on the coefficient b and the nonlinear function f.
5 citations
TL;DR: In this article, a class of nonlocal elliptic equations (−Δ)α/2ρ(x)−b(x),⋅∇ρ (x) = f(x)) on a bounded domain Ω⊂Rd.
Abstract: We study a class of nonlocal elliptic equations (−Δ)α/2ρ(x)−b(x)⋅∇ρ(x)=f(x) on a bounded domain Ω⊂Rd. For f∈Lq(Ω) (q>d/α), by the Lax–Milgram theorem and the De Giorgi iteration, we prove the exist...
4 citations
TL;DR: In this article, the existence and uniqueness of mild solutions for nonlocal PDEs driven by additive white noises on a bounded domain was studied and it was shown that the unique mild solution is almost surely Holder continuous with Holder index $0 <\theta <(1/2-d/(q \alpha))(1\wedge \alpha)$ fixme.
Abstract: We consider nonlocal PDEs driven by additive white noises on ${\mathbb{R}}^{d}$
. For $L^{q}$
integrable coefficients, we derive the existence and uniqueness, as well as Holder continuity, of mild solutions. Precisely speaking, the unique mild solution is almost surely Holder continuous with Holder index $0<\theta <(1/2-d/(q \alpha))(1\wedge \alpha)$
. Moreover, we show that any order $\gamma (< q)$
moment of Holder normal for u on every bounded domain of ${\mathbb{R}}_{+}\times {\mathbb{R}}^{d}$
is finite.
3 citations
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01 Jan 2016
TL;DR: The stochastic differential equations and applications is universally compatible with any devices to read, and an online access to it is set as public so you can get it instantly.
Abstract: stochastic differential equations and applications is available in our digital library an online access to it is set as public so you can get it instantly. Our books collection saves in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the stochastic differential equations and applications is universally compatible with any devices to read.
741 citations
TL;DR: A fast and accurate numerical algorithm is proposed to simulate the nonlocal Fokker–Planck equations on either a bounded or infinite domain and to satisfy a discrete maximum principle and to be convergent.
58 citations
01 Jan 2015
TL;DR: (2 < p < 4) [200].
Abstract: (2 < p < 4) [200]. (Uq(∫u(1, 1)), oq1/2(2n)) [92]. 1 [273, 79, 304, 119]. 1 + 1 [252]. 2 [352, 318, 226, 40, 233, 157, 299, 60]. 2× 2 [185]. 3 [456, 363, 58, 18, 351]. ∗ [238]. 2 [277]. 3 [350]. p [282]. B−L [427]. α [216, 483]. α− z [322]. N = 2 [507]. D [222]. ẍ+ f(x)ẋ + g(x) = 0 [112, 111, 8, 5, 6]. Eτ,ηgl3 [148]. g [300]. κ [244]. L [205, 117]. L [164]. L∞ [368]. M [539]. P [27]. R [147]. Z2 [565]. Z n 2 [131]. Z2 × Z2 [25]. D(X) [166]. S(N) [110]. ∫l2 [154]. SU(2) [210]. N [196, 242]. O [386]. osp(1|2) [565]. p [113, 468]. p(x) [17]. q [437, 220, 92, 183]. R, d = 1, 2, 3 [279]. SDiff(S) [32]. σ [526]. SLq(2) [185]. SU(N) [490]. τ [440]. U(1) N [507]. Uq(sl 2) [185]. φ 2k [283]. φ [553]. φ4 [365]. ∨ [466]. VOA[M4] [33]. Z [550].
35 citations
Posted Content•
TL;DR: This work establishes existence and uniqueness of solutions to evolutive fractional mean field game systems with regularizing coupling for any order of the fractional Laplacian s\in(0,1)$.
Abstract: We establish existence and uniqueness of solutions to evolutive fractional Mean Field Game systems with regularizing coupling, for any order of the fractional Laplacian $s\in(0,1)$. The existence is addressed via the vanishing viscosity method. In particular, we prove that in the subcritical regime $s>1/2$ the solution of the system is classical, while if $s\leq 1/2$ we find a distributional energy solution. To this aim, we develop an appropriate functional setting based on parabolic Bessel potential spaces. We show uniqueness of solutions both under monotonicity conditions and for short time horizons.
16 citations