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Jianhua Huang

Publications and source records attributed to Jianhua Huang.

At least 19 recordsLinked to original sources
arXiv2026

Approximation for stochastic time-space fractional cable equations driven by rough noise

The time-space fractional cable equation arises from extending the generalized fractional Ohm's law to model anomalous diffusion processes. In this paper, we develop and analyze a numerical approximation for stochastic nonlinear time-space fractional cable equation driven by rough noise. The model features both two nonlocal terms in time and one in space. By an operator theoretic approach, we establish the existence, uniqueness and regularity of solutions. To regularize the rough noise, we introduce a spectral Wong-Zakai approximation and derive its convergence rate. For the fully discrete scheme, we employ the spectral Galerkin method for spatial discretization and the backward Euler convolution quadrature for temporal discretization, and we derive error estimates under explicit parameter conditions. Finally, numerical experiments are presented to validate the theoretical convergence rates.

math.NA↗
arXiv2026

Metallic-Phase-Fe$_3$GaTe$_2$ Enabled Interface Engineering for Self-Powered and High-Gain WS$_2$ Photodetectors

Two-dimensional transition-metal dichalcogenides offer strong light-matter interaction but suffer from inefficient carrier separation and contact-related losses in photodetectors. Here, we demonstrate a high-gain WS$_2$/Fe$_3$GaTe$_2$ van der Waals heterostructure photodetector, where metallic Fe$_3$GaTe$_2$ serves as an active interfacial contact. The work-function mismatch, together with interfacial charge redistribution and asymmetric contact geometry, contributes to a built-in field that supports self-powered photodetection at zero bias. Under 450 nm illumination, the device delivers a zero-bias responsivity of 23.5 A/W and an apparent external quantum efficiency of 6.4 x 10$^3$%. At -1 V biasing, the heterostructure exhibits photoresponse at 450, 520 and 633 nm, achieving a responsivity of 9.7 x 10$^3$ A/W and a noise derived specific detectivity of 2.3 x 10$^13$ Jones at 100 Hz under 450 nm illumination. The high photoresponse is attributed to interfacial carrier separation, efficient extraction, and a likely contribution from trap-assisted photogating in multilayer WS$_2$. These results establish Fe$_3$GaTe$_2$-enabled interface engineering as an effective route for self-powered, highly sensitive 2D photodetectors.

cond-mat.mtrl-sci↗
arXiv2026

Almost sure spatial decay and almost sure nonlinear smoothing of some stochastic dispersive equations

In this paper, we consider the almost sure nonlinear smoothing, the almost sure spatial decay and the almost sure uniform convergence of the stochastic mKdV equation and the stochastic cubic KdV-Benjamin-Ono equation. Firstly, for initial data $g\in H^{s}(\mathbb{R})(s\geq\frac{1}{4})$ and $Φ_{2}\in L_{2}^{0,s}$, we prove the local well-posedness for the stochastic cubic KdV-Benjamin-Ono equation. Secondly, we establish the almost sure nonlinear smoothing of the stochastic mKdV equation and the stochastic cubic KdV-Benjamin-Ono equation. Finally, by using the almost sure nonlinear smoothing, we obtain the almost sure spatial decay and the almost sure uniform convergence of the integral term in the pathwise solutions to the stochastic mKdV equation and the stochastic cubic KdV-Benjamin-Ono equation. More precisely, we have the following results: for the stochastic mKdV equation, let $s>\frac{1}{3}$, $f\in H^{s}(\mathbb{R})$ and $Φ_{1}\in L_{2}^{0,s}$. Then, the local pathwise solution $u$ satisfies \begin{eqnarray*} &&\mathbb{P}\Big(\Big\{ω: \lim_{t\rightarrow0}\Big\|u-U(t)f-\int_{0}^{t}U(t-s)Φ_{1}dW(s)\Big\|_{L_{x}^{\infty}}=0\Big\}\Big)=1,\\ &&\mathbb{P}\Big(\Big\{ω: \forall t\in[0,T_ω], \lim_{|x|\rightarrow\infty}\Big(u-U(t)f-\int_{0}^{t}U(t-s)Φ_{1}dW(s)\Big)=0\Big\}\Big)=1. \end{eqnarray*} For the stochastic cubic KdV-Benjamin-Ono equation, let $s>\frac{1}{3}$, $g\in H^{s}(\mathbb{R})$ and $Φ_{2}\in L_{2}^{0,s}$. Then, the local pathwise solution $v$ satisfies \begin{eqnarray*} &&\mathbb{P}\Big(\Big\{ω: \lim_{t\rightarrow0}\Big\|v-V(t)g-\int_{0}^{t}V(t-s)Φ_{2}dW(s)\Big\|_{L_{x}^{\infty}}=0\Big\}\Big)=1,\\ &&\mathbb{P}\Big(\Big\{ω: \forall t\in[0,T_ω],\lim_{|x|\rightarrow\infty}\Big(v-V(t)g-\int_{0}^{t}V(t-s)Φ_{2}dW(s)\Big)=0\Big\}\Big)=1. \end{eqnarray*}

math.AP↗
arXiv2026

Mean-square attractors for non-autonomous Caputo fractional stochastic differential equations

This paper investigates the existence of mean-square attractors for a class of non-autonomous Caputo fractional stochastic differential equations of order $α\in (\frac{1}{2},1)$, with a driving system on a compact base space $P$ and tempered fractional noise. We first construct a mean-square semi-dynamical system on $\mathfrak{C} \times P$ that carries a skew-product semi-flow structure, where $\mathfrak{C}=C(\mathbb{R}^{+}, L^{2}(Ω, \mathcal{F}; \mathbb{R}^d))$ denotes the space of continuous functions from $ \mathbb{R}^{+}$ into $L^2(Ω, \mathcal{F}; \mathbb{R}^d)$. A global forward attracting set is then established in the weak mean-square topology. Moreover, by endowing the function space $\mathfrak{C}_{w}=C(\mathbb{R}^{+}, L^{2}_w(Ω, \mathcal{F}; \mathbb{H}))$ with an appropriate topology that renders it complete, we show that the skew-product semi-flow possesses a bounded and closed mean-square attractor within $\mathfrak{C}_{w} \times P$. It is worth emphasizing that completeness plays a crucial role here: without this property, the attractor need not exist.

math.DS↗
arXiv2026

Ergodicity for stochastic 2D Boussinesq equations with a highly degenerate pure jump Levy noise

This study aims to analyze the ergodicity for stochastic 2D Boussinesq equations and explore the impact of a highly degenerate pure jump Lévy noise acting only in the temperature equation, where this noise could appear on only a few Fourier modes. By leveraging the equi-continuity of the semigroup established through Malliavin calculus and an analysis of stochastic calculus, together with the weak irreducibility of the solution process, we prove the existence and uniqueness of the invariant measure. Moreover, we overcome the main challenge of establishing time asymptotic smoothing properties of the Markovian dynamics corresponding to this system by conducting spectral analysis of the Malliavin covariance matrix.

math.PR↗
arXiv2026

Well-posedness, mean attractors and invariant measures of stochastic discrete long-wave-short-wave resonance equations driven by locally Lipschitz nonlinear noise

This paper is devoted to investigating the random dynamics of stochastic discrete long-wave-short-wave resonance equations, which are characterized by the following features: $(1)$ the equations contain locally Lipschitz nonlinear coupling terms $u_mv_m$ and $(B(|u(t)|^2))_m$ for $m\in \mathbb{Z}$; $(2)$ the nonlinear coefficients of noises satisfy local Lipschitz conditions; and $(3)$ the system couples real and complex equations and is infinite-dimensional. These inherent structural properties prevent the analysis from being carried out in a standard Bochner product space of the same order and make it difficult to directly verify the tightness of the distribution family of solutions. To address these challenges, we adopt a higher-order Bochner product space $L^4(Ω,\ell_c^2)\times L^2(Ω,\ell^2)$ as the phase space and employ the technique of uniform tail-end estimates. The main results include: establishing the global well-posedness of the nonautonomous stochastic discrete long-wave-short-wave resonance equations driven by nonlinear noise in $L^4(Ω,\ell_c^2)\times L^2(Ω,\ell^2)$; based on this, defining the mean random dynamical system and proving the existence and uniqueness of weak $\mathscr{D}$-pullback mean random attractors. When the external forcing terms are independent of time and sample, we investigate the existence of invariant measures for the corresponding autonomous system and examine the limiting behavior of the invariant measure as the noise intensity tends to zero.

math.PR↗
arXiv2026

Admissibility approach to nonuniform exponential dichotomies roughness with nonlocal perturbations

Nonuniform exponential dichotomy serves as an important characteristic of nonuniform hyperbolicity, while admissibility of function classes is often used to characterize nonuniform exponential dichotomy. In this paper, we investigate the preservation of nonuniform exponential dichotomy under certain nonlocal perturbations. By utilizing the concept of admissibility of a pair of function classes, we establish sufficient conditions to ensure that the dichotomy results are consistent with those in the homogeneous situation. These results need to satisfy a smallness integrability condition.

math.DS↗
arXiv2026

Rough differential equations driven by TFBM with Hurst index $H\in (\frac{1}{4}, \frac{1}{3})$

We consider the rough differential equations driven by tempered fractional Brownian motion with Hurst index $H\in (\frac{1}{4}, \frac{1}{3})$ and tempered parameter $λ>0$. First, by means of piecewise linear approximation, we canonically lift the tempered fractional Brownian motion to a three-step geometric rough path in an almost sure sense. Subsequently, employing the Doss-Sussmann technique in conjunction with a greedy sequence of stopping times, we construct a suitable transformation that establishes a bijection between the solution of the rough differential equation and that of an associated ordinary differential equation. This yields the existence and uniqueness of a solution to the original equation. Based on this result and appealing to Gronwall's lemma, we further derive an upper bound for the solution norm, thereby providing a quantitative control on its growth.

math.DS↗
arXiv2026

The Cauchy problem for the generalized KdV equation in the Sobolev space $H^{s}(\mathbf{R})$

In this paper, we are concerned with the Cauchy problem for the generalized KdV equation with random data and rough data. Firstly, when $s\in\mathbf{R}$, by using the initial value randomization technique introduced by Shen et al. (arXiv:2111.11935) and the construction of appropriate auxiliary spaces, we establish the almost sure local well-posedness of the generalized KdV equation in $H^{s}(\mathbf{R})$, which improves Theorem 1.3 of Hwang and Kwak (Proc. Amer. Math. Soc. 146(2018), 267-280.) and Theorem 1.5 of Yan et al.(arXiv:2011.07128.). Secondly, by using the well-posedness results proved in Theorem 1.1, for $f\in H^{s}(\mathbf{R}),\, s\in\mathbf{R}$, we obtain \begin{eqnarray*} &&\mathbb{P}\left(\left\{ω:\lim_{t\rightarrow0}\|u(t,x)-U(t)f^ω(x)\|_{L_{x}^{\infty}}=0\right\}\right)=1, \end{eqnarray*} which improves Theorem 1.6 of Yan et al.(arXiv:2011.07128.). Thirdly, by using the dyadic decomposition and constructing appropriate function spaces, we establish nonlinear smoothing for the generalized KdV equation with rough data. Furthermore, by using this estimate, when data $f\in H^{s}(\mathbf{R})\cap\hat{L}^{\infty}(\mathbf{R}),\, s>\frac{1}{2}-\frac{2}{k+1},\, k\geq4$, we obtain \begin{eqnarray*} &&\lim_{|x|\rightarrow \infty}u(t,x)=0,\quad t\in[0, T]. \end{eqnarray*} In particular, for $f(x)\in H^{s}(\mathbf{R}),\,s>\frac{1}{2}-\frac{2}{k+1},\,k\geq4$, we prove \begin{eqnarray*} &&\lim_{|x|\rightarrow \infty}(u(t,x)-U(t)f(x))=0. \end{eqnarray*} Finally, by using Theorem 1.1, when $f\in H^{s}(\mathbf{R}),\, s\in\mathbf{R}$, we obtain \begin{eqnarray*} &&\mathbb{P}\left(\left\{ω: \forall t\in I_ω, \lim_{|x|\rightarrow \infty}\left(u(t,x)-U(t)f^ω(x)\right)=0\right\}\right)=1. \end{eqnarray*}

math.AP↗
arXiv2026

Finite-dimensional approximations of random attractor for stochastic discrete complex Ginzburg-Landau equations

In this paper, we apply an implicit Euler scheme to discretize the complex Ginzburg-Landau equation and prove the existence of a numerical attractor for the discrete Ginzburg-Landau system. We establish the upper semicontinuity of the numerical attractor with respect to the global attractor as the time step tends to zero. Furthermore, we provide finite-dimensional approximations for three types of attractors (global, numerical, and random), and demonstrate the existence of truncated attractors along with their convergence as the dimension of the state space tends to infinity. Finally, we prove the existence of a random attractor and establish the upper semi-continuity both of the global random attractor and the truncated random attractor.

math.NA↗
arXiv2025

Ergodicity for the fractional Magneto-Hydrodynamic equations driven by a degenerate pure jump noise

This paper is concerned with the ergodicity for stochastic 2D fractional magneto-hydrodynamic equations on the two-dimensional torus driven by a highly degenerate pure jump Lévy noise. We focus on the challenging case where the noise acts in as few as four directions, establishing new results for such high degeneracy. We first employ Malliavin calculus and anticipative stochastic calculus to demonstrate the equi-continuity of the semigroup (or so-called the e-property), and then verify the weak irreducibility of the solution process. Therefore, the uniqueness of invariant measure is proven.

math.PR↗
arXiv2024

Strichartz estimates for orthonormal functions and probabilistic convergence of density functions of compact operators on manifolds

In this paper, we establish some Strichartz estimates for orthonormal functions and probabilistic convergence of density functions related to compact operators on manifolds. Firstly, we present the suitable bound of $\int_{a\leq|s|\leq b}e^{isx}s^{-1+iγ}ds$ for the cases $γ\in \mathbb{R},a\geq0,b>0,$ $γ\in \mathbb{R},γ\neq0,a,b\in \mathbb{R}$ and $γ\in \mathbb{R}$, which extends the result of Page 204 of Vega (199-211,IMA Vol. Math. Appl., 42, 1992.) Secondly, we prove that $\left|γ\int_{a}^{b}e^{isx}s^{-1+iγ}ds\right|\leq C(1+|γ|)^{2}(γ\in \mathbb{R},a,b\in \mathbb{R}),$ where $C$ is independent of $γ,a, b$, which extends Lemma 1 of Bez et al. (Forum of Mathematics, Sigma, 9(2021), 1-52). Thirdly, we extend the result of Theorems 8, 9 of R. Frank, J. Sabin (Amer. J. Math. 139(2017), 1649-1691.) with the aid of the suitable bound of the above complex integrals established in this paper. Fourthly, we establish the Strichartz estimates for orthonormal functions related to Boussinesq operator on the real line for both small time interval and large time interval and on the torus with small time interval; we also establish the convergence result of some compact operators in Schatten norm. Fifthly, we establish the convergence result related to nonlinear part of the solution to some operator equations in Schatten spaces. Finally, inspired by the work of Hadama and Yamamoto (Probabilistic Strichartz estimates in Schatten classes and their applications to Hartree equation, arxiv:2311.02713v1.), for $γ_{0}\in \mathfrak{S}^{2}$, we establish the probabilistic convergence of density functions of compact operator on manifolds with full randomization, which improves the result of Corollary 1.2 of Bez et al. (Selecta Math. 26(2020), 24 pp) in the probabilistic sense.

math.PR↗
arXiv2024

The M33 Synoptic Stellar Survey. III. Miras and LPVs in griJHKs

We present the results of a search for Miras and long-period variables (LPVs) in M33 using griJHKs archival observations from the Canada-France-Hawai'i Telescope. We use multiband information and machine learning techniques to identify and characterize these variables. We recover ~1,300 previously-discovered Mira candidates and identify ~13,000 new Miras and LPVs. We detect for the first time a clear first-overtone pulsation sequence among Mira candidates in this galaxy. We use O-rich, fundamental-mode Miras in the LMC and M33 to derive a distance modulus for the latter of 24.629 +/- 0.046 mag.

astro-ph.GA↗
arXiv2023

Smooth center-stable/unstable manifolds and foliations of stochastic evolution equations with non-dense domain

The current paper is devoted to the asymptotic behavior of a class of stochastic PDE. More precisely, with the help of the theory of integrated semigroups and a crucial estimate of the random Stieltjes convolution, we study the existence and smoothness of center-unstable invariant manifolds and center-stable foliations for a class of stochastic PDE with non-dense domain through the Lyapunov-Perron method. Finally, we give two examples about a stochastic age-structured model and a stochastic parabolic equation to illustrate our results.

math.DS↗
arXiv2021

Mean-square invariant manifolds for ill-posed stochastic evolution equations driven by nonlinear noise

This paper discerns the invariant manifold of a class of ill-posed stochastic evolution equations driven by a nonlinear multiplicative noise. To be more precise, we establish the existence of mean-square random unstable invariant manifold and only mean-square stable invariant set. Due to the lack of the Hille-Yosida condition, we construct a modified variation of constants formula by the resolvent operator. With the price of imposing an unusual condition involving a non-decreasing map, we set up the Lyapunov-Perron method and derive the required estimates. We also emphasize that the Lyapunov-Perron map in the forward time loses the invariant due to the adaptedness, we alternatively establish the existence of mean-square random stable sets.

math.DS↗
arXiv2021

The Cauchy problem for the generalized KdV equation with rough data and random data

In this paper, we consider the Cauchy problem for the generalized KdV equation with rough data and random data. Firstly, we prove that $u(x,t)\longrightarrow u(x,0)$ as $t\longrightarrow0$ for a.e. $x\in \mathbb{R}$ with $u(x,0)\in H^{s}(\mathbb{R})(s>\frac{1}{2}-\frac{2}{k},k\geq8).$ Secondly, we prove that $u(x,t)\longrightarrow e^{-t\partial_{x}^{3}}u(x,0)$ as $t\longrightarrow0$ for a.e. $x\in \mathbb{R}$ with $u(x,0)\in H^{s}(\mathbb{R})(s>\frac{1}{2}-\frac{2}{k},k\geq8).$ Thirdly, we prove that $\lim\limits_{t\longrightarrow 0}\left\|u(x,t)-e^{-t\partial_{x}^{3}}u(x,0)\right\|_{L_{x}^{\infty}}=0$ with $u(x,0)\in H^{s}(\mathbb{R})(s>\frac{1}{2}-\frac{2}{k+1},k\geq5)$. Fourthly, by using Strichartz estimates, probabilistic Strichartz estimates, we establish the probabilistic well-posedness in $H^{s}(\mathbb{R})\left(s>{\rm max} \left\{\frac{1}{k+1}\left(\frac{1}{2}-\frac{2}{k}\right), \frac{1}{6}-\frac{2}{k}\right\}\right)$ with random data. Our result improves the result of Hwang, Kwak (Proc. Amer. Math. Soc. 146(2018), 267-280.). Fifthly, we prove that $\forall ε>0,$ $\forall ω\in Ω_{T},$ $\lim\limits_{t\longrightarrow0}\left\|u(x,t)-e^{-t\partial_{x}^{3}}u^ω(x,0)\right\|_{L_{x}^{\infty}}=0$ with $u(x,0)\in H^{s}(\mathbb{R})(s>\frac{1}{6},k\geq6),$ where ${\rm P}(Ω_{T})\geq 1- C_{1}{\rm exp} \left(-\frac{C}{T^{\fracε{48k}}\|u(x,0)\|_{H^{s}}^{2}}\right)$ and $u^ω(x,0)$ is the randomization of $u(x,0)$. Finally, we prove that $\forall ε>0,$ $\forall ω\in Ω_{T}, \lim\limits_{t\longrightarrow0}\left\|u(x,t)-u^ω(x,0)\right\|_{L_{x}^{\infty}}=0$ with ${\rm P}(Ω_{T})\geq 1- C_{1}{\rm exp} \left(-\frac{C}{T^{\fracε{48k}}\|u(x,0)\|_{H^{s}}^{2}}\right)$ and $u(x,0)\in H^{s}(\mathbb{R})(s>\frac{1}{6},k\geq6)$.

math.AP↗
arXiv2020

Exponential mixing for the fractional Magneto-Hydrodynamic equations with degenerate stochastic forcing

We establish the existence, uniqueness and exponential attraction properties of an invariant measure for the MHD equations with degenerate stochastic forcing acting only in the magnetic equation. The central challenge is to establish time asymptotic smoothing properties of the associated Markovian semigroup corresponding to this system. Towards this aim we take full advantage of the characteristics of the advective structure to discover a novel Hörmander-type condition which only allows for several noises in the magnetic direction.

math.PR↗
arXiv2020

Ergodicity and exponential mixing of the real Ginzburg-Landau equation with a degenerate noiss

In this paper, we establish the existence, uniqueness and attraction properties of an invariant measure for the real Ginzburg-Landau equation in the presence of a degenerate stochastic forcing acting only in four directions. The main challenge is to establish time asymptotic smoothing properties of the Markovian dynamics corresponding to this system. To achieve this, we propose a condition which only requires four noises

math.PR↗