arXiv subjects

Jia Wei He

Publications and source records attributed to Jia Wei He.

4 recordsLinked to original sources

arXiv2026

Long-time dynamics for time-nonlocal generalized Rayleigh-Stokes equations

In this paper, we consider an autonomous semi-dynamical system driven by semilinear time-nonlocal evolution equations, these type equations are used to describe the Rayleigh-Stokes problem for a non-Newtonain fluid to a generalized second grade fluid. We first investigate the global well-posedness of solutions consisting of global Lipschitz condition by a weighted space $\mathcal C$. Utilizing the topology convergence on compact subsets of $\mathcal C$, we construct a semi-dynamical system that satisfies the semi-group structure. It also is shown that this semi-dynamical system has an attracting set when the vector field function satisfies a dissipativity condition and a local Lipschitz condition. With the asymptotic compactness, we also establish the existence of generalized attractors in $\mathcal C_α$ of subspace of $\mathcal C$ the weighted norm.

math.DS↗

arXiv2026

Proximal Projection for Doubly Sparse Regularized Models

Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors can be represented by a Gaussian graphical model, the structure of the predictor graph can be exploited during regularization. Our proposed model exploits this underlying predictor graph structure by decomposing the estimated coefficient vector into a sum of latent variables that correspond to the sum of each node contribution to the coefficient vector. Regularization is then performed on the latent variables rather than on the coefficient vector directly. We use a penalty function that permits a clear user-defined trade-off between the L1 and L2 penalties and propose a novel proximal projection during optimization. Further, our implementation computes the projection operator for the intersection of selected groups, which conserves more computing resources compared to predictor duplication methods, especially for high-dimensional data. Through simulation, we evaluate the performance of our approach under different graph structures and node counts, and present results on real-world data. Results suggest that our method exhibits stable performance relative to other singly or doubly sparse graphical regression models.

stat.ML↗

arXiv2025

Weighted estimates for time-fractional parabolic equations with VMO coefficients

This paper is devoted to the weighted estimates and the solvability of time-fractional parabolic equations. The leading coefficients $a^{ij}(t,x)$ are assumed to have small mean oscillations in $(t,x)$ locally, in both non-divergence and divergence forms, in the whole space. By employing appropriate odd and even extensions along with suitable boundary value conditions, we derive the corresponding results for the half-space. The proofs rely on the application of the Fefferman-Stein theorem and the Hardy-Littlewood maximal function theorem in the context of weighted mixed spaces.

math.AP↗

arXiv2025

Maximal $L_p$-regularity for fractional problem driven by non-autonomous forms

We investigate the maximal $L_p$-regularity in J.L. Lions' problem involving a time-fractional derivative and a non-autonomous form $a(t;\cdot,\cdot)$ on a Hilbert space $H$. This problem says whether the maximal $L_p$-regularity in $H$ hold when $t \mapsto a(t ; u, v)$ is merely continuous or even merely measurable. We prove the maximal $L_p$-regularity results when the coefficients satisfy general Dini-type continuity conditions. In particular, we construct a counterexample to negatively answer this problem, indicating the minimal Hölder-scale regularity required for positive results.

math.CA↗