Sign-changing stationary solutions and blowup for the nonlinear heat equation in a ball

DOI10.1007/s00208-008-0312-6zbMath1168.35022OpenAlexW2103821129MaRDI QIDQ1014219

Flávio Dickstein, Fred B. Weissler, Thierry Cazenave

Publication date: 27 April 2009

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-008-0312-6

zbMATH Keywords

global or blows up in finite timesign-changing regular solutions

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Stability in context of PDEs (35B35)

Related Items (16)

Sign-changing stationary solutions and blowup for the two power nonlinear heat equation in a ball ⋮ Existence and stability of equilibrium solutions of a nonlinear heat equation ⋮ Abstract Volterra integrodifferential equations with applications to parabolic models with memory ⋮ Global existence and blow-up results for a classical semilinear parabolic equation ⋮ Critical spaces for quasilinear parabolic evolution equations and applications ⋮ Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence* ⋮ Asymptotic analysis for radial sign-changing solutions of the Brezis-Nirenberg problem ⋮ Complicated asymptotic behavior of solutions for heat equation in some weighted space ⋮ Blow up of solutions of semilinear heat equations in non radial domains of \(\mathbb{R}^2\) ⋮ Asymptotic analysis and sign-changing bubble towers for Lane-Emden problems ⋮ High initial energy finite time blowup with upper bound of blowup time of solution to semilinear parabolic equations ⋮ Blow-up for sign-changing solutions of the critical heat equation in domains with a small hole ⋮ The evolution to localized and front solutions in a non-Lipschitz reaction-diffusion Cauchy problem with trivial initial data ⋮ Sign-changing stationary solutions and blowup for a nonlinear heat equation in dimension two ⋮ On the structure of global solutions of the nonlinear heat equation in a ball ⋮ Blow up of solutions of semilinear heat equations in general domains

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Finite time blow-up and global solutions for semilinear parabolic equations with initial data at high energy level.
• Asymptotic behavior of some nonlinear heat equations
• On the asymptotic behavior of solutions of certain quasilinear parabolic equations
• A bound for global solutions of semilinear heat equations
• Structural stability for time-periodic one-dimensional parabolic equations
• Existence of solitary waves in higher dimensions
• Some nonexistence and instability theorems for solutions of formally parabolic equations of the form \(Pu_t=-Au+ {\mathfrak F} (u)\)
• Solutions globales d'equations de la chaleur semi lineaires.
• THE OSCILLATION PATTERN OF SOLUTIONS TO PARABOLIC EQUATIONS AS TIME GOES TO INFINITY

This page was built for publication: Sign-changing stationary solutions and blowup for the nonlinear heat equation in a ball