Zhengfang Zhou

activity

20112022

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

16 citations · 54 across the 11 of their papers we have counts for

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Showing math.APShow all

9 papers · 1 filter

math.AP2022

Explicit lower bound of blow-up time in a fully parabolic attraction-repulsion chemotaxis system with nonlinear terms

Minh Le, Zhengfang Zhou

It is known that for the parabolic-elliptic Keller-Segel type system in a smooth bounded domain in 3-dimensional space, the lower bound of a blow-up time of unbounded solution is g…

math.AP2020★ 12 cited

The Monotonicity Principle for Magnetic Induction Tomography

Antonello Tamburrino, Gianpaolo Piscitelli, Zhengfang Zhou

The inverse problem treated in this article consists in reconstructing the electrical conductivity from the free response of the system in the magneto-quasi-stationary (MQS) limit.…

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★ 1 cited

Lattice and Continuum Models Analysis of the Aggregation Diffusion Cell Movement

Lianzhang Bao, Zhengfang Zhou

The process by which one may take a discrete model of a biophysical process and construct a continuous model based on it is of mathematical interest as well as being of practical 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…