相关论文: Forced waves of parabolic-elliptic Keller-Segel mo…

The scalar wave equation is solved using higher order immersed finite elements. We demonstrate that higher order convergence can be obtained. Small cuts with the background mesh are stabilized by adding penalty terms to the weak…

This article deals with the logistic Keller-Segel model \[ \begin{cases} u_t = \Delta u - \chi \nabla\cdot(u\nabla v) + \kappa u - \mu u^2, \\ \\ v_t = \Delta v - v + u \end{cases} \] in bounded two-dimensional domains (with homogeneous…

We consider the linear Schr\"odinger equation under periodic boundary condition, driven by a random force and damped by a quasilinear damping: $$ \frac{d}{dt}u+i\big(-\Delta+V(x)\big) u=\nu \Big(\Delta u-\gr |u|^{2p}u-i\gi |u|^{2q}u \Big)…

Velocity dependent forces varying as $k(\hat{r}/r)(1 - \mu \dot{r}^2 + \gamma r \ddot{r})$ (such as Weber force), here called Weber-like forces, are examined from the point of view of energy conservation and it is proved that they are…

We study the global existence of the parabolic-parabolic Keller-Segel system in $\R^d , d \ge 2$. We prove that initial data of arbitrary size give rise to global solutions provided the diffusion parameter $\tau$ is large enough in the…

The flux-limited Keller--Segel system \begin{align*} \begin{cases} u_t = \Delta u - \chi \nabla \cdot (u|\nabla v|^{p-2}\nabla v), \\[] v_t = \Delta v - v + u^{\theta} \end{cases} \end{align*} is considered under homogeneous Neumann…

We prove a reducibility result for a class of quasi-periodically forced linear wave equations on the $d$-dimensional torus $\mathbb{T}^d$ of the form $$ \partial_{tt} v - \Delta v + \varepsilon {\cal P}(\omega t)[v] = 0 $$ where the…

We numerically simulate, in both the forced and decay regimes, a fourth-order nonlinear diffusion equation derived from the kinetic equation of gravitational wave turbulence in the limit of strongly local quartic interactions. When a…

This paper deals with the long-term behavior of positive solutions for the following parabolic-elliptic chemotaxis competition system with weak singular sensitivity and logistic source \begin{equation} \label{abstract-eq} \begin{cases}…

We study the existence of standing waves for the following weakly coupled system of two Schr\"odinger equations in $\mathbb{R}^N$, $N=2,3$, \[ \begin{cases} i \hslash \partial_{t}\psi_{1}=-\frac{\hslash^2}{2m_{1}}\Delta \psi_{1}+…

We simulate the Gross-Pitaevskii equation to model the development of turbulence in a quantum fluid confined by a cuboid box potential, and forced by shaking along one axis. We observe the development of isotropic turbulence from…

This paper considers the dynamics of the following chemotaxis system $$ \begin{cases} u_t=\Delta u-\chi\nabla (u\cdot \nabla v)+u\left(a_0(t,x)-a_1(t,x)u-a_2(t,x)\int_{\Omega}u\right),\quad x\in \Omega\cr 0=\Delta v+ u-v,\quad x\in \Omega…

This work describes a hyperbolic model for cell-cell repulsion with population dynamics. We consider the pressure produced by a population of cells to describe their motion. We assume that cells try to avoid crowded areas and prefer locally…

We solve the shifted wave equation \begin{align*} \frac{\partial^2}{\partial t^2}\varphi(x,t)=(\Delta_x+\rho^2)\varphi(x,t) \end{align*} on a non compact simply connected harmonic manifold with mean curvature of the horospheres $2\rho>0$.…

This paper deals with the analysis of qualitative properties involved in the dynamics of Keller-Segel type systems in which the diffusion mechanisms of the cells are driven by porous-media flux-saturated phenomena. We study the…

Time-periodic weak solutions for a coupled hyperbolic-parabolic system are obtained. A linear heat and wave equation are considered on two respective $d$-dimensional spatial domains that share a common $(d-1)$-dimensional interface…

Existence of global finite-time bounded entropy solutions to a parabolic-parabolic system proposed in [16] is established in bounded domains under no-flux boundary conditions for nonnegative bounded initial data. This modification of the…

We study a three-wave truncation of a recently proposed damped/forced high-order nonlinear Schr\"odinger equation for deep-water gravity waves under the effect of wind and viscosity. The evolution of the norm (wave-action) and spectral mean…

Faraday waves are a classic example of a system in which an extended pattern emerges under spatially uniform forcing. Motivated by systems in which uniform excitation is not plausible, we study both experimentally and theoretically the…

The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical…