Sho Katayama

activity

20242026

collaborators

4 papers

math.AP2026

Asymptotically self-similar graph-like solutions to a multi-dimensional surface diffusion flow equation under contact angle and no-flux boundary conditions

Yoshikazu Giga, Sho Katayama

This paper studies Mullins' model of thermal grooving which consists of a surface diffusion flow equation with contact angle and no-flux boundary conditions. We consider this probl…

math.AP2025

Remarks on graph-like forward self-similar solutions to the surface diffusion flow equations

Yoshikazu Giga, Sho Katayama

We clarify existence and non-existence of graph-like forward self-similar solutions to the planar surface diffusion equations.

math.AP2025

Infinite multiplicity of positive solutions of an inhomogeneous supercritical elliptic equation on $R^{N}$

Sho Katayama, Yasuhito Miyamoto

We are concerned with positive radial solutions of the inhomogeneous elliptic equation $I^ u + K (∣ x ∣) u^{p} + I^¼ f (∣ x ∣) = 0$ on $R^{N}$ , where $N \geq 3$ , $I^¼ > 0$ and $K$ and $f$ are nonn…

math.AP2024

Large time behavior of exponential surface diffusion flows on $R$

Yoshikazu Giga, Michael GÃ¶sswein, Sho Katayama

We consider a surface diffusion flow of the form $V = \partial_{s}^{2} f (- I^º)$ with a strictly increasing smooth function $f$ typically, $f (r) = e^{r}$ , for a curve with arc-length parameter…

Asymptotically self-similar graph-like solutions to a multi-dimensional surface diffusion flow equation under contact angle and no-flux boundary conditions

Remarks on graph-like forward self-similar solutions to the surface diffusion flow equations

Infinite multiplicity of positive solutions of an inhomogeneous supercritical elliptic equation on RN

Large time behavior of exponential surface diffusion flows on R

Infinite multiplicity of positive solutions of an inhomogeneous supercritical elliptic equation on $R^{N}$

Large time behavior of exponential surface diffusion flows on $R$