Hideyuki Miura

activity

20232025

collaborators

4 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 $u_{t} = Δ u + ∣ u ∣^{p - 1} u$ in possibly non-convex and unbounded domains. Our main result shows the nonexistence of type II blow-up for possibly s…

math.AP2025

Wellposedness of inviscid SQG in the half-plane

In-Jee Jeong, Junha Kim, Hideyuki Miura

We consider the SQG equation without dissipation on the half-plane with Dirichlet boundary condition, and prove local wellposedness in the spaces $W^{3, p}$ and $C^{2, β}$ for any $1…

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.AP2023

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

Hideyuki Miura, Jin Takahashi

We address the critical norm blow-up problem for the nonlinear heat equation $u_{t} - Δ u = ∣ u ∣^{p - 1} u$ in $R^{n} \times (0, T)$ . In the supercritical range $p > (n + 2) / (n - 2)$ , we prove…