4 papers
Spot solutions to a neural field equation on oblate spheroids
Hiroshi Ishii, Riku Watanabe
Understanding the dynamics of excitation patterns in neural fields is an important topic in neuroscience. Neural field equations are mathematical models that describe the excitatio…
Propagating front solutions in a time-fractional Fisher-KPP equation
Hiroshi Ishii
In this paper, we treat the Fisher-KPP equation with a Caputo-type time fractional derivative and discuss the propagation speed of the solution. The equation is a mathematical mode…
Relationship between haptotaxis and chemotaxis in cell dynamics
Hiroshi Ishii, Hideki Murakawa, Yoshitaro Tanaka
The phenomenon where cells with elongated protrusions, such as neurons, communicate by contacting other cells and arrange themselves appropriately is termed cell sorting through ha…
On the approximation of spatial convolutions by PDE systems
Hiroshi Ishii, Yoshitaro Tanaka
This paper considers the approximation of spatial convolution with a given radial integral kernel. Previous studies have demonstrated that approximating spatial convolution using a…