Blow-up set for a superlinear heat equation and pointedness of the initial data

DOI10.3934/dcds.2014.34.4617zbMath1327.35222OpenAlexW2331158275MaRDI QIDQ476571

Yohei Fujishima

Publication date: 2 December 2014

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2014.34.4617

zbMATH Keywords

comparison principleblow-up setsuperlinear heat equationsmall diffusionblow-up problem

Mathematics Subject Classification ID

Blow-up in context of PDEs (35B44) Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian (35K91)

Related Items

Global in time solvability for a semilinear heat equation without the self-similar structure ⋮ Fractional semilinear heat equations with singular and nondecaying initial data ⋮ Blow-up set of type I blowing up solutions for nonlinear parabolic systems ⋮ A limit equation and bifurcation diagrams of semilinear elliptic equations with general supercritical growth ⋮ On the effect of higher order derivatives of initial data on the blow-up set for a semilinear heat equation ⋮ Universal estimates and Liouville theorems for superlinear problems without scale invariance ⋮ Quasi self-similarity and its application to the global in time solvability of a superlinear heat equation ⋮ Solvability of a Semilinear Heat Equation via a Quasi Scale Invariance ⋮ Existence and nonexistence of solutions for the heat equation with a superlinear source term ⋮ Blowing up solutions for nonlinear parabolic systems with unequal elliptic operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Location of the blow-up set for a superlinear heat equation with small diffusion.
• Convergence, asymptotic periodicity, and finite-point blow-up in one- dimensional semilinear heat equations
• Blow-up for a semilinear parabolic equation with large diffusion on \(\mathbb R^N\)
• Blow-up for a semilinear parabolic equation with large diffusion on \(\mathbf R^N\). II.
• On the regularity of the blow-up set for semilinear heat equations
• Blow-up set for type I blowing up solutions for a semilinear heat equation
• Single point blow-up for a semilinear initial value problem
• Life span of solutions with large initial data for a superlinear heat equation
• Blow-up set for a semilinear heat equation with small diffusion
• One dimensional behavior of singular \(n\)-dimensional solutions of semilinear heat equations
• Blow-up time and blow-up set of the solutions for semilinear heat equations with large diffusion.
• Location of blow-up set for a semilinear parabolic equation with large diffusion
• Blow up profile of a solution for a nonlinear heat equation with small diffusion
• Variable instability of a constant blow up solution in a nonlinear heat equation
• Blow-up problems for a semilinear heat equation with large diffusion
• Some blow-up problems for a semilinear parabolic equation with a potential
• Determination of the curvature of the blow-up set and refined singular behavior for a semilinear heat equation
• The blow-up problem for a semilinear parabolic equation with a potential
• Life span of solutions with large initial data in a semilinear parabolic equation
• Nondegeneracy of blowup for semilinear heat equations
• The Blow-Up Time for Solutions of Nonlinear Heat Equations with Small Diffusion
• Higher Dimensional Blow Up for Semilinear Parabolic Equations
• Blow-up set for a semilinear heat equation and pointedness of the initial data
• Life span of solutions for a semilinear parabolic problem with small diffusion