Asymptotics for a parabolic equation with critical exponential nonlinearity

DOI10.1007/s00028-020-00649-zzbMath1470.35077OpenAlexW3109288265WikidataQ115609424 ScholiaQ115609424MaRDI QIDQ2044649

Elide Terraneo, Federica Sani, Michinori Ishiwata, Bernhard Ruf

Publication date: 10 August 2021

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

Full work available at URL: https://doi.org/10.1007/s00028-020-00649-z

zbMATH Keywords

Trudinger-Moser embeddingpotential well argumentdichotomy between finite time blow-up and global existence

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 (2)

Global well-posedness of solutions for 2-D Klein–Gordon equations with exponential nonlinearity ⋮ Global existence and blow-up of solutions to the double nonlinear porous medium equation

Cites Work

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• Existence, non-existence, and uniqueness for a heat equation with exponential nonlinearity in \(\mathbb R^2\)
• Asymptotic behavior and decay estimates of the solutions for a nonlinear parabolic equation with exponential nonlinearity
• A note on the inhomogeneous nonlinear heat equation in two space dimensions
• Local well posedness of a 2D semilinear heat equation
• Energy decay and nonexistence of solution for a reaction-diffusion equation with exponential nonlinearity
• Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions
• Stable and unstable sets for evolution of parabolic and hyperbolic type
• Nonlinear scalar field equations. I: Existence of a ground state
• Existence of a stable set for some nonlinear parabolic equation involving critical Sobolev exponent
• Asymptotic behavior of strong solutions for nonlinear parabolic equations with critical Sobolev exponent
• Semilinear parabolic equation in \(R^N\) associated with critical Sobolev exponent
• Asymptotic behavior of some nonlinear heat equations
• On existence, uniform decay rates and blow up for solutions of the 2-D wave equation with exponential source
• Saddle points and instability of nonlinear hyperbolic equations
• Asymptotic stability and blowing up of solutions of some nonlinear equations
• Existence of solitary waves in higher dimensions
• Convergence to a ground state as a threshold phenomenon in nonlinear parabolic equations
• A sharp Trudinger-Moser type inequality for unbounded domains in \(\mathbb R^2\)
• A nonlinear heat equation with singular initial data
• Type II blow-up for the four dimensional energy critical semi linear heat equation
• Scattering threshold for the focusing nonlinear Klein-Gordon equation
• Trudinger-Moser inequality on the whole plane with the exact growth condition
• Convergence to steady states of solutions of non-autonomous heat equations in \(\mathbb R^N\)
• On global solution of nonlinear hyperbolic equations
• Ground States for Elliptic Equations in $\pmb{\mathbb{R}}^{2}$ with Exponential Critical Growth
• Instability for standing waves of nonlinear Klein-Gordon equations via mountain-pass arguments
• Solutions globales d'equations de la chaleur semi lineaires.
• Seminlinear parabolic equation on bounded domain with critical Sobolev exponent
• The long-time behaviour of solutions to parabolic problems on unbounded intervals: the influence of boundary conditions
• The problem of uniqueness of the limit in a semilinear heat equation
• Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
• Trudinger type inequalities in $\mathbf {R}^N$ and their best exponents
• A Potential Well Argument for a Semilinear Parabolic Equation with Exponential Nonlinearity
• Semilinear parabolic equations involving critical Sobolev exponent: Local and asymptotic behavior of solutions

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