Related papers: Finite-time blow-up prevention in a two-dimensiona…
The study of blow-up solution of time-fractional heat equations is of significant and wide-ranging interest for its multitude of applications. These types of equations are used to model several real problems in science and engineering. This…
We establish criteria on the chemotactic sensitivity $\chi$ for the non-existence of global weak solutions (i.e. \textit{blow-up} in finite time) to a stochastic Keller--Segel model with spatially inhomogeneous, conservative noise on…
We study a nonlinear system coupling the Darcy-Forchheimer-Brinkman equations with a convection-diffusion-reaction equation, arising in reactive transport through porous media. The model features a nonlinear viscosity coupling, Forchheimer…
We consider an initial boundary value problem for a 2x2 system of conservation laws modeling heatless adsorption of a gaseous mixture with two species and instantaneous exchange kinetics, close to the system of Chromatography. In this model…
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…
The present work deals with a Keller-Segel-Navier-Stokes system with potential consumption, under homogeneous Neumann boundary conditions for cell density and chemical signal, and of Dirichlet type for the velocity field, over a bounded…
In this paper we prove finite-time blowup of radially symmetric solutions to the quasilinear parabolic-parabolic two-dimensional Keller-Segel system for any positive mass. This is done in case of nonlinear diffusion and also in the case of…
This paper investigates the global existence and boundedness of solutions in a two-species chemotaxis system with two chemicals and sub-logistic sources. The presence of a sub-logistic source in only one cell density equation effectively…
The present work proceeds to consider the convergence of the solutions to the following doubly degenerate chemotaxis-consumption system \begin{align*} \left\{ \begin{array}{r@{\,}l@{\quad}l@{\,}c} &u_{t}=\nabla\cdot\big(u^{m-1}v\nabla…
We construct examples of finite time singularity from smooth data for linear uniformly parabolic systems in the plane. We obtain similar examples for quasilinear systems with coefficients that depend only on the solution.
This paper considers the homogeneous Neumann initial-boundary value problem for Alopecia Areata chemotaxis model with weakly singular sensitivity. For any appropriately regular initial conditions,it is shown that the problem admits a global…
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…
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:…
We study the Neumann initial-boundary value problem for the parabolic-elliptic chemotaxis system, proposed by J\"ager and Luckhaus (1992). We confirm that their comparison methods can be simplified and refined, applicable to seek the…
This paper studies the following chemotaxis-fluid system in a two-dimensional bounded domain $\Omega$: \begin{equation*} \begin{cases} n_t + u \cdot \nabla n &= \Delta n - \chi \nabla \cdot \left (n \frac{\nabla c}{c^k} \right ) + r n -…
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 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,…
The Keller-Segel equation, a classical chemotaxis model, and many of its variants have been extensively studied for decades. In this work, we focus on 3D Keller-Segel equation with a quadratic logistic damping term $-\mu \rho^2$ (modeling…
In this paper, we consider some blow-up problems for the 1D Euler equation with time and space dependent damping. We investigate sufficient conditions on initial data and the rate of spatial or time-like decay of the coefficient of damping…
We study a chemotaxis-consumption mechanism, in which some chemical signal and cells density interact each other. In order to control the concentration of such a population, sources involving gradient nonlinearities, which introduce a…