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Ruoyang Liu

Publications and source records attributed to Ruoyang Liu.

7 recordsLinked to original sources
arXiv2026

An entropy approach to doubly nonlinear parabolic obstacle problems

This paper studies doubly nonlinear parabolic obstacle problems. We introduce a renormalized entropy formulation in which the reaction measure is encoded by evaluating the entropy multiplier at the obstacle. For diffusion depending only on the gradient and continuous time-independent obstacles, we prove a global $L^1$ comparison estimate, uniqueness of the solution, and a minimality principle among a measure-free entropy supersolution class. For diffusion depending on both the solution and its gradient, we prove existence for continuous time-dependent obstacles with a boundary-controlled decomposition. Using two ordered penalization procedures, we obtain convergence of the approximate solutions and of the corresponding reaction terms. The limiting reaction consists of an absolutely continuous part with bounded density and a finite Radon measure concentrated on a prescribed compact spatial region. A one-sided time regularization yields strong convergence of the gradients and identifies the nonlinear flux. Together, the results yield existence, uniqueness and $L^1$ stability under their common assumptions.

math.AP↗
arXiv2026

Well-posedness and large deviations for the obstacle problem of first-order stochastic conservation laws

This paper studies the obstacle problem for first-order scalar conservation laws driven by multiplicative noise. By adapting a barrier-substitution strategy to the kinetic formulation, we permit the reflection measure to be a general Radon measure and eliminate the usual obstacle-noise compatibility condition. We establish the existence of kinetic solutions for continuous obstacles and further derive $L^1$-contraction and uniqueness under stronger spatial regularity. Moreover, we prove a Freidlin--Wentzell large deviation principle in $L^1(0,T;L^1(\mathbb{T}^N))$. Unlike existing large-deviation arguments based on control-uniform penalization of the obstacle, we work directly with the reflected skeleton equation and retain the possibly singular Radon reflection measure throughout, while a viscous approximation provides the spatial $H^1$-regularity required for compactness before passing to the inviscid limit. Our results provide a hyperbolic counterpart to the large deviation theory for parabolic reflected SPDEs developed by Matoussi, Sabbagh, and Zhang (2021).

math.PR↗
arXiv2026

Well-posedness of the obstacle problem for generalized Dean-Kawasaki equation

We investigate the obstacle problem for generalized Dean--Kawasaki equations driven by correlated conservative noise, establishing the existence, uniqueness, and $L^1$-stability of stochastic kinetic solutions. Our core strategy combines a kinetic characterization of the Skorokhod condition with a precise description of the reflection measure term associated with the obstacle, in which the barrier substitutes the solution. This formulation makes the reflection mechanism explicit at the kinetic level and yields a stable framework adapted to $L^1$ doubling of variables method. Consequently, under a merely continuous obstacle and the same structural assumptions as in the obstacle-free setting, we obtain well-posedness over the full porous-medium regime, covering degenerate diffusion and the critical square-root noise coefficient. This extends the existing theory of obstacle problems for stochastic partial differential equations to a class of degenerate equations with singular diffusion coefficients.

math.PR↗
arXiv2024

Well-posedness of the obstacle problem for stochastic nonlinear diffusion equations: an entropy formulation

In this paper, we establish the existence, uniqueness and stability results for the obstacle problem associated with a degenerate nonlinear diffusion equation perturbed by conservative gradient noise. Our approach revolves round introducing a new entropy formulation for stochastic variational inequalities. As a consequence, we obtain a novel well-posedness result for the obstacle problem of deterministic porous medium equations with nonlinear reaction terms.

math.PR↗
arXiv2023

Entropy solutions to the Dirichlet problem for nonlinear diffusion equations with conservative noise

Motivated by porous medium equations with randomly perturbed velocity field, this paper considers a class of nonlinear degenerate diffusion equations with nonlinear conservative noise in bounded domains. The existence, uniqueness and $L_{1}$-stability of non-negative entropy solutions under the homogeneous Dirichlet boundary condition are proved. The approach combines Kruzhkov's doubling variables technique with a revised strong entropy condition that is automatically satisfied by the solutions of approximate equations.

math.PR↗
arXiv2022

Block-Wise Dynamic-Precision Neural Network Training Acceleration via Online Quantization Sensitivity Analytics

Data quantization is an effective method to accelerate neural network training and reduce power consumption. However, it is challenging to perform low-bit quantized training: the conventional equal-precision quantization will lead to either high accuracy loss or limited bit-width reduction, while existing mixed-precision methods offer high compression potential but failed to perform accurate and efficient bit-width assignment. In this work, we propose DYNASTY, a block-wise dynamic-precision neural network training framework. DYNASTY provides accurate data sensitivity information through fast online analytics, and maintains stable training convergence with an adaptive bit-width map generator. Network training experiments on CIFAR-100 and ImageNet dataset are carried out, and compared to 8-bit quantization baseline, DYNASTY brings up to $5.1\times$ speedup and $4.7\times$ energy consumption reduction with no accuracy drop and negligible hardware overhead.

cs.LG↗