Related papers: Comparison Methods for a Keller--Segel-type Model …
In this paper, we consider global existence of classical solutions to the following kinetic model of pattern formation \begin{equation} \begin{cases} u_t=\Delta (\gamma (v)u)+\mu u(1-u) -\Delta v+v=u \end{cases} \qquad (0.1)…
This paper is concerned with global solvability of a fully parabolic system of Keller--Segel-type involving non-monotonic signal-dependent motility. First, we prove global existence of classical solutions to our problem with generic…
This paper deals with classical solutions to the parabolic-parabolic system \begin{align*} \begin{cases} u_t=\Delta (\gamma (v) u ) &\mathrm{in}\ \Omega\times(0,\infty), \\[1mm] v_t=\Delta v - v + u &\mathrm{in}\ \Omega\times(0,\infty),…
This paper investigates an initial-Neumann boundary value problem for a Keller--Segel system with parabolic-parabolic-ODE coupling. The model incorporates a signal-dependent, non-increasing motility function that, through indirect signal…
In this paper, we consider the initial Neumann boundary value problem for a degenerate kinetic model of Keller--Segel type. The system features a signal-dependent decreasing motility function that vanishes asymptotically, i.e., degeneracies…
This paper establishes the global uniform-in-time boundedness of solutions to the following Keller-Setel system with signal-dependent diffusion and chemotaxis \begin{equation}\left\{ \begin{array}{ll} u_t=\nabla\cdot(\gamma(v)\nabla u -…
A fully parabolic chemotaxis model of Keller-Segel type with local sensing is considered. The system features a signal-dependent asymptotically non-degenerate motility function, which accounts for a repulsion-dominated chemotaxis. Global…
In the present article we consider several issues concerning the doubly parabolic Keller-Segel system in the plane, when the initial data belong to critical scaling-invariant Lebesgue spaces. More specifically, we analyze the global…
In this paper, existence of a strong global solution for all finite time is derived for the Kirchhoff's model of parabolic type. Based on exponential weight function, some new regularity results which reflect the exponential decay property…
This paper is devoted to global existence of weak solutions to the following degenerate kinetic model of chemotaxis \begin{equation} \begin{cases}\label{chemo0} u_t=\Delta (\gamma (v)u) \tau v_{t}=\Delta v-v+u \end{cases} \end{equation}in a…
This paper aims at providing a first step toward a qualitative theory for a new class of chemotaxis models derived from the celebrated Keller-Segel system, with the main novelty being that diffusion is nonlinear with flux delimiter…
It is known that solutions of the parabolic elliptic Keller-Segel equations in the two dimensional plane decay, as time goes to infinity, provided the initial data admits sub-critical mass and finite second moments, while such solution…
Global existence is established for classical solutions to a chemotaxis model with signal-dependent motility for a general class of motility functions $\gamma$ which may in particular decay in an arbitrary way at infinity. Assuming further…
We consider a Keller-Segel model coupled to the incompressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criteria for both cases that…
In this paper, we investigate the Cauchy problem of the parabolic-parabolic Keller-Segel system with the logistic-type term $au-bu^\gamma$ on $\mathbb{R}^N, N\geq2$. We discuss the global boundedness of classical solutions with nonnegative…
An initial-Neumann boundary value problem for a Keller--Segel system with density-suppressed motility and source terms is considered. Infinite-time blowup of the classical solution was previously observed for its source-free version when…
In this paper, we consider an initial-Neumann boundary value problem for a parabolic-elliptic Keller-Segel system with signal-dependent motility and a source term. Previous research has rigorously shown that the source-free version of this…
In this paper, we investigate global existence of large solutions for the parabolic-elliptic Keller-Segel system in the homogeneous Besov type spaces. A class of initial data was presented, generating a global smooth solution although the…
In the current paper, we consider the following parabolic-elliptic semilinear Keller-Segel model on $\mathbb{R}^{N}$, \begin{equation*} \begin{cases} u_{t}=\nabla\cdot (\nabla u-\chi u\nabla v)+a u -b u^2, \quad x\in\mathbb{R}^N,\,\, t>0\cr…
This paper is concerned with the global boundedness and blowup of solutions to the Keller-Segel system with density-dependent motility in a two-dimensional bounded smooth domain with Neumman boundary conditions. We show that if the motility…