Global existence and blow-up of solutions for the heat equation with exponential nonlinearity

DOI10.1016/J.JDE.2018.01.048zbMath1428.35152OpenAlexW2790990370WikidataQ130095884 ScholiaQ130095884MaRDI QIDQ1706624

Yohei Fujishima

Publication date: 22 March 2018

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2018.01.048

zbMATH Keywords

blow-upnonlinear heat equationexponential nonlinearityglobal in time existenceforward self-similar solution

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Reaction-diffusion equations (35K57) Initial value problems for second-order parabolic equations (35K15) Blow-up in context of PDEs (35B44) Self-similar solutions to PDEs (35C06)

Related Items (5)

Blow-up analysis for heat equation with a nonlocal weighted exponential boundary flux ⋮ Complex valued semi-linear heat equations in super-critical spaces \(E^s_\sigma\) ⋮ Quasi self-similarity and its application to the global in time solvability of a superlinear heat equation ⋮ Existence and blow-up of solutions in Hénon-type heat equation with exponential nonlinearity ⋮ Global well-posedness for the nonlinear damped wave equation with logarithmic type nonlinearity

Cites Work

• Unnamed Item
• Unnamed Item
• The role of forward self-similar solutions in the Cauchy problem for semilinear heat equations
• Stability of steady states of the Cauchy problem for the exponential reaction-diffusion equation
• Global, unbounded solutions to a parabolic equation
• An ODE approach to the multiplicity of self-similar solutions for semi-linear heat equations
• Global Existence, Large Time Behavior and Life Span of Solutions of a Semilinear Parabolic Cauchy Problem
• On the stability and instability of positive steady states of a semilinear heat equation in ℝn
• On the Cauchy Problem for Reaction-Diffusion Equations
• Domain of existence and blowup for the exponential reaction-diffusion equation
• Continuation of blowup solutions of nonlinear heat equations in several space dimensions
• On the nonlinear equations Δ𝑢+𝑒^{𝑢}=0 and ∂𝑣/∂𝑡=Δ𝑣+𝑒^{𝑣}
• Further study on a nonlinear heat equation

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