Kentarou Fujie

This paper deals with the chemotaxis system\[\begin{cases}u_t=\Delta u - \nabla \cdot (u\nabla v),\qquad x\in \Omega, \ t>0, \\v_t=\Delta v + wz,\qquad x\in \Omega, \ t>0, \\w_t=-wz,\qquad x\in \Omega, \ t>0, \\z_t=\Delta z - z + u, \qquad x\in \Omega, \ t>0,\end{cases}\]in a smoothly bounded domain $\Omega \subset \mathbb{R}^n$, $n \le 3$,that has recently been proposed as a model for tumor invasionin which the role of an active extracellular matrix is accounted for. It is shown that for any ch

This paper deals with the parabolic–elliptic Keller–Segel system with signal-dependent chemotactic sensitivity function, under homogeneous Neumann boundary conditions in a smooth bounded domain , with initial data satisfying u0 ≥ 0 and . The chemotactic sensitivity function χ(v) is assumed to satisfy The global existence of weak solutions in the special case is shown by Biler (Adv. Math. Sci. Appl. 1999; 9:347–359). Uniform boundedness and blow-up of radial solutions are studied by Nagai and Sen

This paper deals with positive radially symmetric solutions of the Neumann boundary value problem for the fully parabolic chemotaxis system, {ut=Δu−∇⋅(u∇χ(v))in Ω×(0,∞),τvt=Δv−v+uin Ω×(0,∞), in a ball with general sensitivity function satisfying and decaying property (), parameter and nonnegative radially symmetric initial data.

This paper is concerned with the parabolic-elliptic Keller-Segel system with signal-dependent sensitivity $\chi(v)$,\begin{align*}\begin{cases}u_t=\Delta u - \nabla \cdot ( u \nabla \chi(v))&\mathrm{in}\ \Omega\times(0,\infty), \\0=\Delta v -v+u&\mathrm{in}\ \Omega\times(0,\infty),\end{cases}\end{align*}under homogeneous Neumann boundary condition in a smoothly bounded domain$\Omega \subset \mathbb{R}^2$with nonnegative initial data $u_0 \in C^{0}(\overline{\Omega})$, $\not\equiv 0$.  &nbsp

This paper deals with time-global solutions to the parabolic system under the homogeneous Neumann boundary conditions in a bounded and convex domain () with smooth boundary . Here τ is a positive parameter, χ is a smooth function on satisfying and is a pair of nonnegative initial data.

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