Optimal Liouville theorems for superlinear parabolic problems

DOI10.1215/00127094-2020-0096zbMath1469.35071arXiv2003.13223OpenAlexW3155679627MaRDI QIDQ2037854

Pavol Quittner

Publication date: 8 July 2021

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.13223

zbMATH Keywords

scaling invariant nonlinear parabolic equations and systems

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) A priori estimates in context of PDEs (35B45) Second-order parabolic equations (35K10) Second-order parabolic systems (35K40) Blow-up in context of PDEs (35B44) Semilinear parabolic equations (35K58) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (15)

Liouville theorems for parabolic systems with homogeneous nonlinearities and gradient structure ⋮ Entire solutions with moving singularities for a semilinear heat equation with a critical exponent ⋮ Blow-up rate of sign-changing solutions to nonlinear parabolic systems in domains ⋮ A triviality result for semilinear parabolic equations ⋮ Blow-up rate of sign-changing solutions to nonlinear parabolic systems ⋮ Bubble towers in the ancient solution of energy-critical heat equation ⋮ Universal estimates and Liouville theorems for superlinear problems without scale invariance ⋮ Monotonicity of solutions for weighted fractional parabolic equations on the upper half space ⋮ Semilinear Li and Yau inequalities ⋮ A Liouville type theorem for a scaling invariant parabolic system with no gradient structure ⋮ Asymptotic symmetry and monotonicity of solutions for weighted fractional parabolic equations ⋮ Liouville-type theorem for one-dimensional porous medium systems with sources ⋮ Nonexistence of solutions for indefinite fractional parabolic equations ⋮ Liouville theorems for fractional parabolic equations ⋮ A Liouville theorem for ancient solutions to a semilinear heat equation and its elliptic counterpart

Cites Work

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