Xin Yang

activity

20122021

most citedA Paradox of State-Dependent Diffusion and How to Resolve It

49 citations · 83 across the 9 of their papers we have counts for

collaborators

9 papers

math.AP2021

Smooth solutions to the heat equation which are nowhere analytic in time

Xin Yang, Chulan Zeng, Qi S. Zhang

The existence of smooth but nowhere analytic functions is well-known (du Bois-Reymond, Math. Ann., 21(1):109-117, 1883). However, smooth solutions to the heat equation are usually…

math.AP2019

Prevention of blowup via Neumann heat kernel

Xin Yang, Zhengfang Zhou

Consider the heat equation $u_{t} - Δ u = 0$ on a bounded $C^{2}$ domain $Ω$ in $R^{n} (n \geq 2)$ with any positive initial data. If a superlinear radiation law $\frac{\partial u}{\…

math.AP2018★ 5 cited

Lifespan estimates via Neumann heat kernel

Xin Yang, Zhengfang Zhou

This paper studies the lower bound of the lifespan $T^{*}$ for the heat equation $u_{t} = Δ u$ in a bounded domain $Ω \subset R^{n} (n \geq 2)$ with positive initial data $u_{0}$ a…

math.AP2017★ 9 cited

Improvements on lower bounds for the blow-up time under local nonlinear Neumann conditions

Xin Yang, Zhengfang Zhou

This paper studies the heat equation $u_{t} = Δ u$ in a bounded domain $Ω \subset R^{n} (n \geq 2)$ with positive initial data and a local nonlinear Neumann boundary condition: the…

math.AP2016★ 1 cited

Lower bounds for the blow-up time of the heat equation in convex domains with local nonlinear boundary conditions

Xin Yang, Zhengfang Zhou

This paper studies the lower bound for the blow-up time $T^{*}$ of the heat equation $u_{t} = Δ u$ in a bounded convex domain $Ω$ in $R^{N} (N \geq 2)$ with positive initial data…

math.AP2015★ 3 cited

Revisit to Fritz John's paper on the blow-up of nonlinear wave equations

Xin Yang, Zhengfang Zhou

In Fritz John's famous paper (1979), he discovered that for the wave equation $□ u = ∣ u ∣^{p}$ , where $1 < p < 1 + 2$ and $□$ denoting the d'Alembertian, there is no global solut…

math.AP2015★ 16 cited

Blow-up problems for the heat equation with a local nonlinear Neumann boundary condition

Xin Yang, Zhengfang Zhou

This paper estimates the blow-up time for the heat equation $u_{t} = Δ u$ with a local nonlinear Neumann boundary condition: The normal derivative $\partial u / \partial n = u^{q}$ on $Γ_{1…

math.NA2014

Convergence of a Metropolized Integrator for Stochastic Differential Equations with Variable Diffusion Coefficient

Paul Tupper, Xin Yang

We present an explicit method for simulating stochastic differential equations (SDEs) that have variable diffusion coefficients and satisfy the detailed balance condition with resp…

math.DS2012★ 49 cited

A Paradox of State-Dependent Diffusion and How to Resolve It

P. F. Tupper, Xin Yang

Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient…