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math.AP2025
Reaction, diffusion and nonlocal interactions in high-dimensional space
Hiroshi Ishii, Yoshitaro Tanaka
In this paper we consider the mathematical relationship between nonlocal interactions of convolution type and multiple diffusive substances in high dimensions. Motivated by that th…
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…
math.AP2024
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…