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math.AP2026
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…
math.AP2026
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…
math.AP2025
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…