Junichi Harada

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math.AP2025

Oscillatory behavior of solutions to the critical Fujita equation in 6D

Junichi Harada

Long time dynamics of solutions to the 6D energy critical heat equation $u_{t} = I^ u + ∣ u ∣^{p - 1} u$ on $R^{6} \times (0, \infty)$ is investigated. It is shown that there exists a radially sym…

math.AP2025

Dynamics near the ground state for the Sobolev critical Fujita type heat equation in 6D

Junichi Harada

This paper investigates the asymptotic behavior of solutions to $u_{t} = I^ u + ∣ u ∣^{p - 1} u$ in the Sobolev critical case. Our main result is a classification of the dynamics near the grou…

math.AP2024

Stability of nondegenerate ODE type blowup for the Fujita type heat equation

Junichi Harada

The asymptotic bahavior of blowup solutions to the Fujita type heat equation $u_{t} = I^ u + ∣ u ∣^{p - 1} u$ is studied. This equation admits the ODE type blowup given by $u(x,t)=(p-1)^\frac{…