20 citations · 22 across the 10 of their papers we have counts for
11 papers
A Step in the Right Place: Understanding and Optimizing Timestep Placement in Continuous Diffusion Language Models
Shutian Zheng, Zhihong Yu, Linye Wei +2
Continuous diffusion language models represent an emerging paradigm for language modeling. They generate text in parallel by iteratively refining continuous representations and map…
Blow-up at arbitrary energy levels for a strongly damped viscoelastic wave equation with a variable-exponent logarithmic source
Menglan Liao, Mingxue Zhang
We study a strongly damped viscoelastic wave equation with a logarithmic source whose measurable exponent satisfies . An optimal pointwise correction to…
Divergence-form equations admitting nowhere Lipschitz weak solutions
Menglan Liao, Baisheng Yan
We study a class of partial differential equations in divergence form that admit highly irregular Lipschitz weak solutions. By reformulating these divergence-form equations as a fi…
Stabilization for a degenerate wave equation with time-varying delay in the boundary control input
Menglan Liao
A degenerate wave equation with time-varying delay in the boundary control input is considered. The well-posedness of the system is established by applying the semigroup theory. Th…
Decay rates for a variable-coefficient wave equation with nonlinear time-dependent damping
Menglan Liao
In this paper, a class of variable-coefficient wave equations equipped with time-dependent damping and the nonlinear source is considered. We show that the total energy of the syst…
On behavior of solutions to a Petrovsky equation with damping and variable-exponent source
Menglan Liao, Zhong Tan
This paper deals with the following Petrovsky equation with damping and nonlinear source \[u_{tt}+Δ^2 u-M(\|\nabla u\|_2^2)Δu-Δu_t+|u_t|^{m(x)-2}u_t=|u|^{p(x)-2}u\] under initial-b…
Asymptotic stability for a class of viscoelastic equations with general relaxation functions and the time delay
Menglan Liao, Zhong Tan
The goal of the present paper is to study the viscoelastic wave equation with the time delay \[ |u_t|^ρu_{tt}-Δu-Δu_{tt}+\int_0^tg(t-s)Δu(s)ds+μ_1u_t(x,t)+μ_2 u_t(x,t-τ)=b|u|^{p-2}…
Energy decay rates of solutions to a viscoelastic wave equation with variable exponents and weak damping
Menglan Liao, Bin Guo, Xiangyu Zhu
The goal of the present paper is to study the asymptotic behavior of solutions for the viscoelastic wave equation with variable exponents \[ u_{tt}-Δu+\int_0^tg(t-s)Δu(s)ds+a|u_t|^…
Global existence and blow-up of solutions to a class of non-Newton filtration equations with singular potential and logarithmic nonlinearity
Menglan Liao, Zhong Tan
In this paper, a class of non-Newton filtration equations with singular potential and logarithmic nonlinearity under initial-boundary condition is investigated. Based on potential…
Classification of blow-up and global existence of solutions to an initial problem
Bin Guo, Jingjing Zhang, Menglan Liao
The aim of this paper is to apply the modified potential well method and some new differential inequalities to study the asymptotic behavior of solutions to the initial homogeneous…
On weak closure of some diffusion equations
Menglan Liao, Lianzhang Bao, Baisheng Yan
We study the closure of approximating sequences of some diffusion equations under certain weak convergence. A specific description of the closure under weak -convergence is gi…