J. Takahashi

collaborators

3 papers

math.AP2025

Blow-up rate for the subcritical semilinear heat equation in non-convex domains

Hideyuki Miura, Jin Takahashi, Erbol Zhanpeisov

We consider the semilinear heat equation $u_{t} = I^ u + ∣ u ∣^{p - 1} u$ in possibly non-convex and unbounded domains. Our main result shows the nonexistence of type II blow-up for possibly…

math.AP2024

Critical norm blow-up rates for the energy supercritical nonlinear heat equation

Tobias Barker, Hideyuki Miura, Jin Takahashi

We prove the first classification of blow-up rates of the critical norm for solutions of the energy supercritical nonlinear heat equation, without any assumptions such as radial sy…

math.AP2024

Moving gradient singularity for the evolutionary $p$ -Laplace equation

Erik Lindgren, Jin Takahashi

We consider the evolutionary $p$ -Laplace equation in $R^{n}$ . For $p > n$ , we construct a solution $u$ with a moving gradient singularity in the sense that $|\nabla u(x,t)|\to…

Blow-up rate for the subcritical semilinear heat equation in non-convex domains

Critical norm blow-up rates for the energy supercritical nonlinear heat equation

Moving gradient singularity for the evolutionary p-Laplace equation

Moving gradient singularity for the evolutionary $p$ -Laplace equation