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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-lambda v +mu u,quad xin mathbb{R}^N, end{cases}(1) end{equation} where $chi, mu,lambda,a,$ and $b$ are positive numbers, and $tauge 0$. Among others, it is proved that if $b>2chimu$ and $tau geq frac{1}{2}(1-frac{lambda}{a})_{+} ,$ then for every $cge 2sqrt{a}$, (1) has a traveling wave solution $(u,v)(t,x)=(U^{tau,c}(xcdotxi-ct),V^{tau,c}(xcdotxi-ct))$ ($forall, xiinmathbb{R}^N$) connecting the two constant steady states $(0,0)$ and $(frac{a}{b},frac{mu}{lambda}frac{a}{b})$, and there is no such solutions with speed $c$ less than $2sqrt{a}$, which improves considerably the results established in cite{SaSh3}, and shows that (1) has a minimal wave speed $c_0^*=2sqrt a$, which is independent of the chemotaxis.
In this paper, we study traveling wave solutions of the chemotaxis systems begin{equation} begin{cases} u_{t}=Delta u -chi_1 abla( u abla v_1)+chi_2 abla(u abla v_2 )+ u(a -b u), qquad xinmathbb{R} taupartial_tv_1=(Delta- lambda_1 I)v_1+ mu_1 u, q
In this paper we consider a stochastic Keller-Segel type equation, perturbed with random noise. We establish that for special types of random pertubations (i.e. in a divergence form), the equation has a global weak solution for small initial data. Fu
We show that the Keller-Segel model in one dimension with Neumann boundary conditions and quadratic cellular diffusion has an intricate phase transition diagram depending on the chemosensitivity strength. Explicit computations allow us to find a myri
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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 may take