4 papers
math.AP2026
One-bubble solution with maximum points escaping to infinity for the energy-critical heat equation in
Junichi Harada, Qidi Zhang
We investigate the existence of a one-bubble solution with maximum points escaping to infinity for the energy-critical heat equation in dimension five. The key point of the constru…
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 on is investigated. It is shown that there exists a radially symm…
math.AP2024
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 in the Sobolev critical case. Our main result is a classification of the dynamics near the groun…
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 is studied. This equation admits the ODE type blowup given by $u(x,t)=(p-1)^\frac{1…