Jin Takahashi

collaborators

2 papers

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…

math.AP2022

Solvability of a semilinear heat equation on Riemannian manifolds

Jin Takahashi, Hikaru Yamamoto

We study the solvability of the initial value problem for the semilinear heat equation $u_{t} - Δ u = u^{p}$ in a Riemannian manifold $M$ with a nonnegative Radon measure $μ$ on $M$ as init…