University of New England

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19932026

most citedSpreading and vanishing in nonlinear diffusion problems with free boundaries

217 citations

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math.AP2020

The Stefan problem for the Fisher-KPP equation with unbounded initial range

Weiwei Ding, Yihong Du, Zongming Guo

We consider the nonlinear Stefan problem $$ \left \{ \begin{array} {ll} -d Δu=a u-b u^2 \;\; & \mbox{for } x \in Ω(t), \; t>0, \\ u=0 \mbox{ and } u_t=μ|\nabla_x u |^2 \;\;&\mbox{f…

math.AP2019

A free boundary problem for spreading under shifting climate

Yuanyang Hu, Xinan Hao, Xianfa Song +1

In this paper we consider a free boundary problem which models the spreading of an invasive species whose spreading is enhanced by the changing climate. We assume that the climate…

math.AP2019★ 42 cited

Monotonicity of the principal eigenvalue for a linear time-periodic parabolic operator

Shuang Liu, Yuan Lou, Rui Peng +1

We investigate the effect of frequency on the principal eigenvalue of a time-periodic parabolic operator with Dirichlet, Robin or Neumann boundary conditions. The monotonicity and…

math.AP2018★ 1 cited

The Fisher-KPP equation over simple graphs: Varied persistence states in river networks

Yihong Du, Bendong Lou, Rui Peng +1

In this article, we study the growth and spread of a new species in a river network with two or three branches via the Fisher-KPP advection-diffusion equation over some simple grap…

math.AP2018★ 3 cited

Logarithmic corrections in Fisher-KPP type Porous Medium Equations

Yihong Du, Fernando Quiros, Maolin Zhou

We consider the large time behaviour of solutions to the porous medium equation with a Fisher-KPP type reaction term and nonnegative, compactly supported initial function in $L^\in…

math.AP2018★ 2 cited

The dynamics of a Fisher-KPP nonlocal diffusion model with free boundaries

Jiafeng Cao, Yihong Du, Fang Li +1

We introduce and study a class of free boundary models with "nonlocal diffusion", which are natural extensions of the free boundary models in Du and Lin [17] and elsewhere, where "…

math.AP2018

Infinitely many non-radial solutions to a critical equation on annulus

Yuxia Guo, Benniao Li, Angela Pistoia +1

In this paper, we build infinitely many non-radial sign-changing solutions to the critical problem: \begin{equation*} \left\{\begin{array}{rlll} -Δu&=|u|^{\frac{4}{N-2}}u, &\hbox{…

math.AP2017★ 7 cited

Radial terrace solutions and propagation profile of multistable reaction-diffusion equations over $R^{N}$

Yihong Du, Hiroshi Matano

We study the propagation profile of the solution $u (x, t)$ to the nonlinear diffusion problem $u_{t} - Δ u = f (u) (x \in R^{N}, t > 0)$ , $u (x, 0) = u_{0} (x) (x \in R^{N})$ , where $…

math.AP2016★ 2 cited

Spreading in space-time periodic media governed by a monostable equation with free boundaries, Part 1: Continuous initial functions

Weiwei Ding, Yihong Du, Xing Liang

We aim to classify the long-time behavior of the solution to a free boundary problem with monostable reaction term in space-time periodic media. Such a model may be used to describ…

math.AP2016★ 2 cited

A diffusive Fisher-KPP equation with free boundaries and time-periodic advections

Ningkui Sun, Bendong Lou, Maolin Zhou

We consider a reaction-diffusion-advection equation of the form: $u_{t} = u_{xx} - β (t) u_{x} + f (t, u)$ for $x \in (g (t), h (t))$ , where $β (t)$ is a $T$ -periodic function representing the intens…

math.AP2015★ 5 cited

Spreading in a shifting environment modeled by the diffusive logistic equation with a free boundary

Yihong Du, Lei Wei, Ling Zhou

We investigate the influence of a shifting environment on the spreading of an invasive species through a model given by the diffusive logistic equation with a free boundary. When t…

math.AP2015★ 4 cited

Semi-wave and spreading speed for the diffusive competition model with a free boundary

Yihong Du, Mingxin Wang, Maolin Zhou

We determine the asymptotic spreading speed of an invasive species, which invades the territory of a native competitor, governed by a diffusive competition model with a free bounda…

math.AP2015★ 25 cited

A KPP road-field system with spatially periodic exchange terms

Thomas Giletti, Léonard Monsaingeon, Maolin Zhou

We take interest in a reaction-diffusion system which has been recently proposed [11] as a model for the effect of a road on propagation phenomena arising in epidemiology and ecolo…

math.AP2015★ 4 cited

Equations involving fractional Laplacian operator: Compactness and application

Shusen Yan, Jianfu Yang, Xiaohui Yu

In this paper, we consider the following problem involving fractional Laplacian operator: \begin{equation}\label{eq:0.1} (-Δ)^α u= |u|^{2^*_α-2-\varepsilon}u + λu\,\, {\rm in}\,\,…

math.AP2015★ 8 cited

Long time behavior of solutions of Fisher-KPP equation with advection and free boundaries

Hong Gu, Bendong Lou, Maolin Zhou

We consider Fisher-KPP equation with advection: $u_{t} = u_{xx} - β u_{x} + f (u)$ for $x \in (g (t), h (t))$ , where $g (t)$ and $h (t)$ are two free boundaries satisfying Stefan conditions. This eq…

math.AP2013★ 8 cited

Entire solutions for a class of elliptic equations involving $p$ -biharmonic operator and Rellich potentials

Mousomi Bhakta

We study existence, multiplicity and qualitative properties of entire solutions for a noncompact problem related to p-biharmonic type equations with weights. More precisely, we dea…

math.AP2013★ 3 cited

Critical $O (d)$ -equivariant biharmonic maps

Matthew K. Cooper

We study $O (d)$ -equivariant biharmonic maps in the critical dimension. A major consequence of our study concerns the corresponding heat flow. More precisely, we prove that blowup o…

math.AP2013★ 217 cited

Spreading and vanishing in nonlinear diffusion problems with free boundaries

Yihong Du, Bendong Lou

We study nonlinear diffusion problems of the form $u_{t} = u_{xx} + f (u)$ with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, w…

math.AP2008

On the Webster scalar curvature problem on the CR sphere with a cylindrical-type symmetry

Daomin Cao, Shuangjie Peng, Shusen Yan

By variational methods, for a kind of Webster scalar curvature problems on the CR sphere with cylindrically symmetric curvature, we construct some multi-peak solutions as the param…

math.AP2008

Infinitely many positive solutions for the nonlinear Shcrodinger equations in $R^{N}$

Juncheng Wei

We consider the following nonlinear problem in $R^{N}$ $$\label{eq} - Δu +V(|y|)u=u^{p},\quad u>0 {in} \R^N, u \in H^1(\R^N) $$ where $V (r)$ is a positive function, $1<p <\frac{N+2}…

math.AP2008

Infinitely many solution for prescribed curvature problem on $S^{N}$

Juncheng Wei, Shusen Yan

We consider the following prescribed scalar curvature problem on $S^{N}$ (*)$$\left\{\begin{array}{l} - Δ_{S^N} u + \frac{N(N-2)}{2} u = \tilde{K} u^{\frac{N+2}{N-2}} {on} S^N, u >0…

The Stefan problem for the Fisher-KPP equation with unbounded initial range

A free boundary problem for spreading under shifting climate

Monotonicity of the principal eigenvalue for a linear time-periodic parabolic operator

The Fisher-KPP equation over simple graphs: Varied persistence states in river networks

Logarithmic corrections in Fisher-KPP type Porous Medium Equations

The dynamics of a Fisher-KPP nonlocal diffusion model with free boundaries

Infinitely many non-radial solutions to a critical equation on annulus

Radial terrace solutions and propagation profile of multistable reaction-diffusion equations over RN

Spreading in space-time periodic media governed by a monostable equation with free boundaries, Part 1: Continuous initial functions

A diffusive Fisher-KPP equation with free boundaries and time-periodic advections

Spreading in a shifting environment modeled by the diffusive logistic equation with a free boundary

Semi-wave and spreading speed for the diffusive competition model with a free boundary

A KPP road-field system with spatially periodic exchange terms

Equations involving fractional Laplacian operator: Compactness and application

Long time behavior of solutions of Fisher-KPP equation with advection and free boundaries

Entire solutions for a class of elliptic equations involving p-biharmonic operator and Rellich potentials

Critical O(d)-equivariant biharmonic maps

Spreading and vanishing in nonlinear diffusion problems with free boundaries

On the Webster scalar curvature problem on the CR sphere with a cylindrical-type symmetry

Infinitely many positive solutions for the nonlinear Shcrodinger equations in RN

Infinitely many solution for prescribed curvature problem on SN

Radial terrace solutions and propagation profile of multistable reaction-diffusion equations over $R^{N}$

Entire solutions for a class of elliptic equations involving $p$ -biharmonic operator and Rellich potentials

Critical $O (d)$ -equivariant biharmonic maps

Infinitely many positive solutions for the nonlinear Shcrodinger equations in $R^{N}$

Infinitely many solution for prescribed curvature problem on $S^{N}$