6 papers
Bifurcation structure and mesa pattern formation in a one-component nonlocal adhesion model with population pressure and degenerate mobility
Shimpei Makida, Hideki Murakawa
We analyze pattern formation from a homogeneous steady state in a one-component nonlocal adhesion model with population pressure and degenerate mobility. First, using linear stabil…
Convergence of a discrete-in-time Approximation to a Degenerate Parabolic-Hyperbolic System
Julia Hauser, Hideki Murakawa, Markus Schmidtchen
In this paper we consider an implicit semi-discrete approximation of a degenerate reaction-cross-diffusion system. Due to the symmetry in the parabolic part, this system is known t…
Reaction-Diffusion System Approximation to the Fast Diffusion Equation
Hideki Murakawa, Florian Salin
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation meth…
Relationship between haptotaxis and chemotaxis in cell dynamics
Hiroshi Ishii, Hideki Murakawa, Yoshitaro Tanaka
Cell sorting mediated by direct cell--cell contact or cellular protrusions can be described by nonlocal cell--cell adhesion models of haptotaxis type, whereas communication through…
Keller-Segel type approximation for nonlocal Fokker-Planck equations in one-dimensional bounded domain
Hideki Murakawa, Yoshitaro Tanaka
Numerous evolution equations with nonlocal convolution-type interactions have been proposed. In some cases, a convolution was imposed as the velocity in the advection term. Motivat…
Numerical approximation of a reaction-diffusion system with fast reversible reaction
R. Eymard, D. Hilhorst, M. Olech
We consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction. We deduce from a priori estimates that the approximate solution converges…