Related papers: Chemotaxis systems with singular sensitivity and l…

In the current paper, we consider the following parabolic-parabolic chemotaxis system with logistic source on $\mathbb{R}^{N}$, \begin{equation} \begin{cases} u_t=\Delta u-\chi\nabla\cdot ( u\nabla v) + u(a-bu),\quad…

In this paper, we are concerned with a class of parabolic-elliptic chemotaxis systems encompassing the prototype $$\left\{\begin{array}{lll} &u_t = \nabla\cdot(\nabla u-\chi u\nabla v)+f(u), & x\in \Omega, t>0, \\[0.2cm] &0= \Delta v…

In this paper, we study the following chemotaxis--haptotaxis system with (generalized) logistic source $$ \left\{\begin{array}{ll} u_t=\Delta u-\chi\nabla\cdot(u\nabla v)- \xi\nabla\cdot(u\nabla w)+u(a-\mu u^{r-1}-w),…

We consider the following chemotaxis system under homogeneous Neumann boundary conditions in a smooth, open, bounded domain $\Omega \subset \mathbb{R}^n$ with $n \geq 3$: \begin{equation*} \begin{cases} u_t = \Delta u - \chi \nabla \cdot…

For given total mass $m>0$ we show unique solvability of the stationary chemotaxis-consumption model \[ \begin{cases} 0= \Delta u - \chi \nabla \cdot (\frac{u}{v} \nabla v) \\ 0= \Delta v - uv \\ \int_\Omega u = m \end{cases} \] under…

In present paper, we consider a chemotaxis consumption system with density-signal governed sensitivity and logistic source: $u_t=\Delta u-\nabla\cdot(\frac{S(u)}{v}\nabla v)+ru-\mu u^2$, $v_t=\Delta v-uv$ in a smooth bounded domain…

This work studies the chemotaxis-haptotaxis system $$\left\{ \begin{array}{ll} u_t= \Delta u - \chi \nabla \cdot (u\nabla v) - \xi \nabla \cdot (u\nabla w) + \mu u(1-u-w), &\qquad x\in \Omega, \, t>0, \\[1mm] v_t=\Delta v-v+u, &\qquad x\in…

In this paper we consider the zero-flux chemotaxis-system \begin{equation*} \begin{cases} u_{t}=\Delta u-\nabla \cdot (u \chi(v)\nabla v) & \textrm{in}\quad \Omega\times (0,\infty), \\ 0=\Delta v-v+g(u) & \textrm{in}\quad \Omega\times…

This paper deals with the fully parabolic attraction-repulsion chemotaxis system with signal-dependent sensitivities, \begin{align*} \begin{cases} u_t=\Delta u-\nabla \cdot (u\chi(v)\nabla v) +\nabla \cdot (u\xi(w)\nabla w), &x \in \Omega,\…

In the current paper, we study stability, bifurcation, and spikes of positive stationary solutions of the following parabolic-elliptic chemotaxis system with singular sensitivity and logistic source, \begin{cases} u_t=u_{xx}-\chi…

This paper deals with the problem of global solvability and boundedness of classical solutions to a fully parabolic chemotaxis system with singular sensitivity in any dimensional setting. In particular, We show that the system…

We consider classical solutions to the chemotaxis system with logistic source $f(u) := au-\mu u^2$ under nonlinear Neumann boundary condition $\frac{\partial u}{ \partial \nu } = |u|^{p}$ with $p>1$ in a smooth convex bounded domain $\Omega…

This series of papers is concerned with the global solvability, boundedness, regularity, and uniqueness of weak solutions to the following parabolic-parabolic chemotaxis system with a logistic source and chemical consumption:…

This paper deals with the following attraction-repulsion chemotaxis system with nonlocal logistic source and sublinear productions \[ \left\{ \begin{array}{rrll} &&u_t = d_1 \Delta u-\chi \nabla\cdot(u^k \nabla v)+\xi \nabla\cdot(u^k \nabla…

We prove existence of global weak solutions to the chemotaxis system $ u_t=\Delta u - \nabla\cdot (u\nabla v) +\kappa u -\mu u^2 $ $ v_t=\Delta v-v+u $ under homogeneous Neumann boundary conditions in a smooth bounded convex domain…

We show the existence of locally bounded global solutions to the chemotaxis system \[ u_t = \nabla\cdot(D(u)\nabla u) - \nabla\cdot(\frac{u}{v} \nabla v) \] \[ v_t = \Delta v - uv \] with homogeneous Neumann boundary conditions and suitably…

Introducing a suitable solution concept, we show that in bounded smooth domains $\Omega\subset \mathbb{R}^n$, $n\ge 1$, the initial boundary value problem for the chemotaxis system \begin{align*} u_t&=\Delta u…

We consider a parabolic-elliptic system of partial differential equations with chemotaxis and logistic growth given by the system $$ \left\{ \begin{array}{l} u_t -\Delta (u \gamma(v)= \mu u(1-u), \\ - \Delta v +v=u, \end{array} \right. $$…

We consider the chemotaxis model \begin{align*} \begin{cases} u_t = \Delta u - \nabla \cdot (u \nabla v), \\ v_t = \Delta v - vw, \\ w_t = -\delta w + u \end{cases} \end{align*} in smooth, bounded domains $\Omega \subset \mathbb R^n$, $n…

This paper studies the chemotaxis-haptotaxis system \begin{equation}\nonumber \left\{ \begin{array}{llc} u_t=\Delta u-\chi\nabla\cdot(u\nabla v)-\xi\nabla\cdot(u\nabla w)+\mu u(1-u-w), &(x,t)\in \Omega\times (0,T),\\ v_t=\Delta v-v+u,…