Front propagation for nonlinear diffusion equations on the hyperbolic space

DOI10.4171/JEMS/529zbMath1322.35065OpenAlexW2272321081MaRDI QIDQ2350333

Hiroshi Matano, Fabio Punzo, Tesei, Alberto

Publication date: 19 June 2015

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/jems/529

zbMATH Keywords

extinctionAllen-Cahn equationcritical velocityFujita exponentKolmogorov-Petrovskii-Piskunov equation

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Reaction-diffusion equations (35K57)

Related Items (10)

Multiplicative controllability for semilinear reaction-diffusion equations with finitely many changes of sign ⋮ Asymptotically almost periodic solutions to parabolic equations on the real hyperbolic manifold ⋮ Bistable reaction equations with doubly nonlinear diffusion ⋮ Blow-up on metric graphs and Riemannian manifolds ⋮ Construction of a stable periodic solution to a semilinear heat equation with a prescribed profile ⋮ Propagation and extinction of fronts for semilinear parabolic equations on Riemannian manifolds ⋮ Asymptotic behavior of spreading fronts in the anisotropic Allen-Cahn equation on \(\mathbb{R}^n\) ⋮ Invasion fronts on graphs: the Fisher-KPP equation on homogeneous trees and Erdős-Réyni graphs ⋮ Spreading properties for SIR models on homogeneous trees ⋮ Porous medium equations on manifolds with critical negative curvature: unbounded initial data

Cites Work

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• Uniqueness and nonuniqueness of solutions to parabolic problems with singular coefficients
• The Fujita exponent for the Cauchy problem in the hyperbolic space
• Large time behavior of disturbed planar fronts in the Allen-Cahn equation
• Asymptotic behaviour of a reaction-diffusion equation in higher space dimensions
• Elementary geometry in hyperbolic space
• Lectures on hyperbolic geometry
• The approach of solutions of nonlinear diffusion equations to travelling front solutions
• Multidimensional nonlinear diffusion arising in population genetics
• Serrin's result for hyperbolic space and sphere
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds

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