Related papers: Finite-time blow-up in a two species chemotaxis-co…

This paper investigates the finite-time blow-up phenomena to a quasilinear two-species chemotaxis system with two chemicals \begin{align}\tag{$\star$} \begin{cases} u_t = \nabla \cdot \left(D_1(u) \nabla u\right) - \nabla \cdot \left(u…

This paper deals with the quasilinear degenerate chemotaxis system with flux limitation \begin{align*} \begin{cases} u_t = \nabla\cdot\left(\dfrac{u^p \nabla u}{\sqrt{u^2 + |\nabla u|^2}} \right) -\chi \nabla\cdot\left( \dfrac{u^q\nabla…

This paper is concerned with a three-component chemotaxis model accounting for indirect signal production,reading as $u_t = \nabla\cdot(\nabla u - u\nabla v)$,$v_t = \Delta v - v + w$ and $0 = \Delta w - w + u$,posed in a ball of $\mathbb…

Perhaps the most classical diffusion model for chemotaxis is the Keller-Segel system $\begin{equation} \begin{cases} u_{t} =\Delta u - \nabla \cdot(u \nabla v) \ \ \ \text{in } \mathbb{R}^2\times(0,T),\\[5pt] v =…

This paper deals with the two-species chemotaxis-competition models \begin{align*} \begin{cases} u_t = d_1 \Delta u - \chi_1 \nabla \cdot (u \nabla w) + \mu_1 u (1- u^{\kappa_1-1} - a_1 v^{\lambda_1-1}), &\quad x \in \Omega,\ t>0,\\ % v_t =…

This paper is concerned with a parabolic-parabolic-parabolic chemotaxis system with indirect signal production, modelling the impact of phenotypic heterogeneity on population aggregation \begin{equation*} \begin{cases} u_t = \Delta u -…

This paper investigates the repulsive chemotaxis-consumption model \begin{align*} \partial_t u &= \nabla \cdot (D(u) \nabla u) + \nabla \cdot (u \nabla v), \\ 0 &= \Delta v - uv \end{align*} in an $n$-dimensional ball, $n \ge 3$, where the…

We investigate the following two-species chemotaxis system with two chemicals involving flux-limitation \begin{align}\tag{$\star$} \begin{cases} u_t = \Delta u - \nabla \cdot \left(u(1+|\nabla v|^2)^{-\frac{p}{2}}\nabla v\right), & x \in…

We show that the attraction-repulsion chemotaxis system \begin{equation*} \begin{cases} u_t = \Delta u - \chi\nabla\cdot(u\nabla v_1) + \xi\nabla\cdot(u\nabla v_2)\\ \partial_t v_1 = \Delta v_1 - \beta v_1 + \alpha u \\ \partial_t v_2 =…

In this paper, we introduce the nonlinear diffusion term $\nabla\cdot(D(u)\nabla u)$ into the chemotaxis-May-Nowak model to investigate the effects of $D(u)$ and chemotaxis on the global existence, boundedness, and finite time blow-up of…

In this paper we consider nonnegative solutions of the following parabolic-elliptic cross-diffusion system \begin{equation*} \left\{ \begin{array}{l} \begin{aligned} &u_t = \Delta u - \nabla(u f(|\nabla v|^2 )\nabla v), \\[6pt] &0= \Delta v…

This paper deals with unbounded solutions to the following zero--flux chemotaxis system \begin{equation}\label{ProblemAbstract} \tag{$\Diamond$} \begin{cases} % about u u_t=\nabla \cdot [(u+\alpha)^{m_1-1} \nabla u-\chi u(u+\alpha)^{m_2-2}…

The Neumann initial-boundary problem for the chemotaxis system \begin{align} \label{prob:abstract} \tag{$\star$} \begin{cases} u_t = \Delta u - \nabla \cdot (u \nabla v) + \kappa(|x|) u - \mu(|x|) u^p, \\ 0 = \Delta v -…

We study the chemotaxis model $\partial$ t u = div($\nabla$u -- u$\nabla$w) + $\theta$v -- u in (0, $\infty$) x $\Omega$, $\partial$ t v = u -- $\theta$v in (0, $\infty$) x $\Omega$, $\partial$ t w = D$\Delta$w -- $\alpha$w + v in (0,…

This paper is concerned with the attraction-repulsion chemotaxis system with superlinear logistic degradation, \begin{align*} \begin{cases} u_t = \Delta u - \chi \nabla\cdot(u \nabla v) + \xi \nabla\cdot (u \nabla w) + \lambda u - \mu u^k,…

In this study, we explore the quasilinear two-species chemotaxis system with two chemicals \begin{align}\tag{$\star$} \begin{cases} u_t = \nabla \cdot(D(u)\nabla u) - \nabla \cdot \left(S(u) \nabla v\right), & x \in \Omega, \ t > 0, \\ 0 =…

This paper deals with the fully parabolic attraction-repulsion chemotaxis system \begin{align*} u_t=\Delta u-\chi\nabla \cdot (u\nabla v)+\xi \nabla\cdot(u \nabla w), \quad v_t=\Delta v-v+u, \quad w_t=\Delta w-w+u, \quad x \in \Omega,\ t>0…

The Neumann problem in balls $\Omega\subset\mathbb{R}^n$, $n\in\{3,4\}$, for the chemotaxis system \begin{equation*} \left\{ \begin{array}{ll} u_t = \Delta u - \nabla \cdot (u\nabla v), \\[1mm] 0 = \Delta v - \mu^{(w)}(t) + w, \quad…

\indent In this paper, we study a class of parabolic-elliptic Keller-Segel systems with diffusion sensitivity dependent on spatial position, given by type \begin{equation} \left\{ \begin{array}{ll} u_{t} = \bigtriangledown\cdot(|x|^{\beta}…

Perhaps the most classical diffusion model for chemotaxis is the Keller-Segel system \begin{equation}\tag{$\ast$} \label{ks0} \left\{ \begin{aligned} u_t =&\; \Delta u - \nabla \cdot(u \nabla v) \quad in {\mathbb R}^2\times(0,\infty),\\ v…