Localized Solutions of a Semilinear Parabolic Equation with a Recurrent Nonstationary Asymptotics

DOI10.1137/140958566zbMath1316.35148OpenAlexW1987680771MaRDI QIDQ5174887

Eiji Yanagida, Peter Poláčik

Publication date: 19 February 2015

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/24d6759c0e5e769345479278b77b732296e5b384

zbMATH Keywords

asymptotic behaviorsemilinear parabolic equationlocalized solutionsnonconvergent solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial value problems for second-order parabolic equations (35K15)

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Threshold behavior and non-quasiconvergent solutions with localized initial data for bistable reaction-diffusion equations ⋮ Nonlinear Diffusion Problems with Free Boundaries: Convergence, Transition Speed, and Zero Number Arguments ⋮ Front propagation in both directions and coexistence of traveling fronts and pulses ⋮ Nonexistence of radial time-periodic solutions of reaction-diffusion equations with generic nonlinearities ⋮ Planar Propagating Terraces and the Asymptotic One-dimensional Symmetry of Solutions of Semilinear Parabolic Equations ⋮ Threshold phenomena for symmetric-decreasing radial solutions of reaction-diffusion equations ⋮ Sharp thresholds between finite spread and uniform convergence for a reaction-diffusion equation with oscillating initial data ⋮ Localized and expanding entire solutions of reaction-diffusion equations ⋮ Examples of bounded solutions with nonstationary limit profiles for semilinear heat equations on \({\mathbb{R}}\)

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