The role of forward self-similar solutions in the Cauchy problem for semilinear heat equations

DOI10.1016/J.JDE.2012.08.013zbMath1270.35164OpenAlexW2044160747MaRDI QIDQ713336

Yūki Naito

Publication date: 26 October 2012

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

Full work available at URL: https://doi.org/10.1016/j.jde.2012.08.013

zbMATH Keywords

asymptotic behaviorblow-upself-similar solutionsemilinear heat equationsub- and super-solutionsstability and instability

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Blow-up in context of PDEs (35B44) Semilinear parabolic equations (35K58) Self-similar solutions to PDEs (35C06)

Related Items (5)

Quasi self-similarity and its application to the global in time solvability of a superlinear heat equation ⋮ Existence of sign-changing solutions for the Hénon type parabolic equation with singular initial data ⋮ Existence and blow-up of solutions in Hénon-type heat equation with exponential nonlinearity ⋮ Global existence and blow-up of solutions for the heat equation with exponential nonlinearity ⋮ Asymptotically self-similar behaviour of global solutions for semilinear heat equations with algebraically decaying initial data

Cites Work

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• Convergence to self-similar solutions for a semilinear parabolic equation
• Remarks on the large time behaviour of a nonlinear diffusion equation
• Asymptotically self-similar global solutions of the nonlinear Schrödinger and heat equations
• Existence and non-existence of global solutions for a semilinear heat equation
• On bounded and unbounded global solutions of a supercritical semilinear heat equation
• Regular self-similar solutions of the nonlinear heat equation with initial data above the singular steady state
• Non-uniqueness of solutions to the Cauchy problem for semilinear heat equations with singular initial data
• Asymptotic behavior of solutions of a semilinear heat equation with subcritical nonlinearity
• Quasilinear Dirichlet problems driven by positive sources
• An ODE approach to the multiplicity of self-similar solutions for semi-linear heat equations
• Self-similar solutions for a semilinear heat equation with critical Sobolev exponent
• 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
• 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
• Asymptotically self-similar global solutions of a general semilinear heat equation

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