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

DOI10.1007/s40818-020-00088-6zbMath1469.35056arXiv2002.00528OpenAlexW3088664300MaRDI QIDQ2040250

Junichi Harada

Publication date: 12 July 2021

Published in: Annals of PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.00528

zbMATH Keywords

matched asymptotic expansion

Mathematics Subject Classification ID

Initial value problems for second-order parabolic equations (35K15) Blow-up in context of PDEs (35B44) Semilinear parabolic equations (35K58)

Related Items

Blowup solutions for the nonlocal shadow limit model of a singular Gierer-Meinhardt system with critical parameters ⋮ Bubble towers in the ancient solution of energy-critical heat equation ⋮ Construction of blow-up solution for 5-dimensional critical Fujita-type equation with different blow-up speed ⋮ Gradient profile for the reconnection of vortex lines with the boundary in type-II superconductors ⋮ Existence of blowup solutions to the semilinear heat equation with double power nonlinearity ⋮ Decay rates for the 4D energy‐critical nonlinear heat equation ⋮ Optimal Liouville theorems for superlinear parabolic problems ⋮ Type II blow-up for a semilinear heat equation with potential

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Blowup profile for a complex valued semilinear heat equation
• Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions
• Stability of the blow-up profile for equations of the type \(u_ t=\Delta u+| u| ^{p-1}u\)
• Type II blow-up mechanisms in a semilinear heat equation with critical Joseph-Lundgren exponent
• Type II blow-up for the four dimensional energy critical semi linear heat equation
• Infinite-time blow-up for the 3-dimensional energy-critical heat equation
• Green's function and infinite-time bubbling in the critical nonlinear heat equation
• A higher speed type II blowup for the five dimensional energy critical heat equation
• Type II finite time blow-up for the energy critical heat equation in \(\mathbb{R}^4\)
• Type II blow-up in the 5-dimensional energy critical heat equation
• Type II blow-up mechanisms in a semilinear heat equation with Lepin exponent
• Blow-up behaviour of one-dimensional semilinear parabolic equations
• Type-II blowup for a semilinear heat equation
• Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity
• Nondegeneracy of blowup for semilinear heat equations
• Dynamics of Threshold Solutions for Energy-Critical Wave Equation
• Asymptotically self‐similar blow‐up of semilinear heat equations
• Higher Dimensional Blow Up for Semilinear Parabolic Equations
• Refined asymptotics for the blowup of u_t — δu = u^p
• On Nonexistence of type II blowup for a supercritical nonlinear heat equation
• Blow up rate for semilinear heat equations with subcritical nonlinearity
• Universality in blow-up for nonlinear heat equations