J. Harada

activity

20132022

most citedA type II blowup for the six dimensional energy critical heat equation

5 citations · 10 across the 6 of their papers we have counts for

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math.AP2022

Existence of blowup solutions to the semilinear heat equation with double power nonlinearity

Junichi Harada

We consider the semilinear heat equation $u_{t} = Δ u + ∣ u ∣^{p - 1} u - ∣ u ∣^{q - 1} u$ in $R^{n} \times (0, T)$ , where $n = 5$ , $p = \frac{n + 2}{n - 2}$ and $q \in (0, 1)$ . By the presence of $-|u|^{q-…

math.AP2020★ 5 cited

A type II blowup for the six dimensional energy critical heat equation

Junichi Harada

We study blowup solutions of the 6D energy critical heat equation $u_{t} = Δ u + ∣ u ∣^{p - 1} u$ in $R^{n} \times (0, T)$ . A goal of this paper is to show the existence of type II blowup solution…

math.AP2019★ 3 cited

A higher speed type II blowup for the five dimensional energy critical heat equation

Junichi Harada

This paper is concerned with blow-up solutions of the five dimensional energy critical heat equation $u_{t} = Δ u + ∣ u ∣^{\frac{4}{3}} u$ . A goal of this paper is to show the existence of typ…

math.AP2013

Non self-similar blow-up solutions to the heat equation with nonlinear boundary conditions

Junichi Harada

This paper is concerned with finite blow-up solutions of the heat equation with nonlinear boundary conditions. It is known that a rate of blow-up solutions is the same as the self-…

math.AP2013★ 2 cited

Blow-up behavior of solutions to the heat equation with nonlinear boundary conditions

Junichi Harada

We study the asymptotic behavior of blow-up solutions of the heat equation with nonlinear boundary conditions. In particular, we classify the asymptotic behavior of blow-up solutio…