ﻻ يوجد ملخص باللغة العربية
We study a doubly tactic resource consumption model bess left{begin{array}{lll} u_t=tr u- ablacd(u abla w),[1mm] v_t=tr v- ablacd(v abla u)+v(1-v^{beta-1}),[1mm] w_t=tr w-(u+v)w-w+r end{array}right. eess in a smooth bounded domain $ooinR^2$ with homogeneous Neumann boundary conditions, where $rin C^1(barOmegatimes[0,infty))cap L^infty(Omegatimes(0,infty))$ is a given nonnegative function fulfilling bess int_t^{t+1}ii| nsqrt{r}|^2<yy for all t>0. eess It is shown that, firstly, if $beta>2$, then the corresponding Neumann initial-boundary problem admits a global bounded classical solution. Secondly, when $beta=2$, the Neumann initial-boundary problem admits a global generalized solution.
This paper investigates a high-dimensional chemotaxis system with consumption of chemoattractant begin{eqnarray*} left{begin{array}{l} u_t=Delta u- ablacdot(u abla v), v_t=Delta v-uv, end{array}right. end{eqnarray*} under homogeneous boundary conditi
This paper is concerned with traveling wave solutions of the following full parabolic Keller-Segel chemotaxis system with logistic source, begin{equation} begin{cases} u_t=Delta u -chi ablacdot(u abla v)+u(a-bu),quad xinmathbb{R}^N cr tau v_t=Delta v
The chemotaxis--Navier--Stokes system begin{equation*}label{0.1} left{begin{array}{ll} n_t+ucdot abla n=triangle n-chi ablacdotp left(displaystylefrac n {c} abla cright)+n(r-mu n), c_t+ucdot abla c=triangle c-nc, u_t+ (ucdot abla) u=Delta
In this contribution, we study a class of doubly nonlinear elliptic equations with bounded, merely integrable right-hand side on the whole space $mathbb{R}^N$. The equation is driven by the fractional Laplacian $(-Delta)^{frac{s}{2}}$ for $sin (0,1]$
This paper addresses the existence and regularity of weak solutions for a fully parabolic model of chemotaxis, with prevention of overcrowding, that degenerates in a two-sided fashion, including an extra nonlinearity represented by a $p$-Laplacian di