相关论文: Singular measure traveling waves in an epidemiolog…
We study a non-linear and non-local evolution equation for curves obtained as the sharp interface limit of a phase-field model for crawling motion of eukaryotic cells on a substrate. We establish uniqueness of solutions to the sharp…
We analyze the propagation of an incident electromagnetic wave in a purely-time modulated medium. Precisely, we assume that the permeability is unchanged while the permittivity has a multiple-step profile in time and uniformly constant in…
In this paper we present a thorough study on the existence of traveling waves in a mathematical model of dispersal in a partially sedentary age-structured population. This type of model was first proposed by Veit and Lewis in [{\it Am.…
We are concerned with a class of degenerate diffusion equations with time delay describing population dynamics with age structure. In our recent study [{\em Nonlinearity}, 33 (2020), 4013--4029], we established the existence and uniqueness…
We examine travelling wave solutions of the Porous-Fisher model, $\partial_t u(x,t)= u(x,t)\left[1-u(x,t)\right] + \partial_x \left[u(x,t) \partial_x u(x,t)\right]$, with a Stefan-like condition at the moving front, $x=L(t)$. Travelling…
Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…
We have measured pulsed microwave transmission through quasi-1D samples with lengths up to three localization lengths. For times approaching four times the diffusion time \tau_D, transmission is diffusive in accord with the self-consistent…
We investigate a reaction-diffusion-advection equation of the form $u_t-u_{xx}+\beta u_x=f(u)$ $(t>0,\,0<x<h(t))$ with mixed boundary condition at $x=0$ and a free boundary condition at $x=h(t)$. Such a model may be applied to describe the…
We consider an epidemic model with direct transmission given by a system of nonlinear partial differential equations and study the existence of traveling wave solutions. When the basic reproductive number of the considered model is less…
Oncolytic virotherapy (OVT) is a promising cancer treatment strategy in which engineered viruses selectively infect and destroy tumor cells. Motivated by the biological mechanisms underlying viral spread and tumor invasion into the tissue,…
This paper is concerned with the non-existence of time-periodic traveling wave solution with speed less than the critical speed for diffusive Kermack-McKendrick epidemic model incorporating seasonality and nonlocal interactions induced by…
We study the propagation properties of nonnegative and bounded solutions of the class of reaction-diffusion equations with nonlinear fractional diffusion: $u_{t} + (-\Delta)^s (u^m)=f(u)$. For all $0<s<1$ and $m> m_c=(N-2s)_+/N $, we…
This paper is concerned with a lattice dynamical system modeling the evolution of susceptible and infective individuals at discrete niches. We prove the existence of traveling waves connecting the disease-free state to non-trivial leftover…
We study a two-dimensional free boundary problem that models motility of eukaryotic cells on substrates. This problem consists of an elliptic equation describing the flow of cytoskeleton gel coupled with a convection-diffusion PDE for the…
We study an integro-differential equation that describes the slow erosion of granular flow. The equation is a first order non-linear conservation law where the flux function includes an integral term. We show that there exist unique…
We consider a reaction-diffusion process with retardation. The particles, immersed in traps initially, remain inactive until another particle is annihilated spontaneously with a rate $\lambda$ at a certain point $\vec x$. In that case the…
Living cells employ excitable reaction-diffusion waves for internal cellular functions, in which curvature-inducing proteins are often involved. However, the role of their mechanochemical coupling is not well understood. Here, we report the…
We consider a partial differential equation model for the growth of heterogeneous cell populations subdivided into multiple distinct discrete phenotypes. In this model, cells preferentially move towards regions where they feel less…
In this paper we present a thorough study on the existence of traveling waves in a mathematical model of dispersal in a partially sedentary age-structured population. This type of model was first proposed by Veit and Lewis in [{\it Am.…
We consider a family of controlled reaction-diffusion equations, describing the spatial spreading of an invasive biological species. For a given propagation speed $c\in{I\!\!R}$, we seek a control with minimum cost, which achieves a…