Stability of radially symmetric travelling waves in reaction-diffusion equations

DOI10.1016/j.anihpc.2003.04.002zbMath1066.35018OpenAlexW2055433313MaRDI QIDQ1888404

Violaine Roussier

Publication date: 23 November 2004

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_2004__21_3_341_0

zbMATH Keywords

spherically symmetric perturbations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) Initial value problems for second-order parabolic equations (35K15)

Related Items (18)

Travelling waves for adaptive grid discretizations of reaction diffusion systems. I: Well-posedness ⋮ Curvature-driven front propagation through planar lattices in oblique directions ⋮ Spreading sets and one-dimensional symmetry for reaction-diffusion equations ⋮ Long time behavior of entire solutions to bistable reaction diffusion equations ⋮ Target patterns in a 2D array of oscillators with nonlocal coupling ⋮ Spiral Waves: Linear and Nonlinear Theory ⋮ Travelling waves for adaptive grid discretizations of reaction diffusion systems. III: Nonlinear theory ⋮ Large time behavior of the solutions with spreading fronts in the Allen-Cahn equations on \(\mathbb{R}^n\) ⋮ A non-local cross-diffusion model of population dynamics II: exact, approximate, and numerical traveling waves in single- and multi-species populations ⋮ Symmetrization and anti-symmetrization in parabolic equations ⋮ Propagation of Reactions in Inhomogeneous Media ⋮ Asymptotic behavior of spreading fronts in the anisotropic Allen-Cahn equation on \(\mathbb{R}^n\) ⋮ Threshold phenomena for symmetric-decreasing radial solutions of reaction-diffusion equations ⋮ Domain walls dynamics in a nanowire subject to an electric current ⋮ Dynamics of curved travelling fronts for the discrete Allen-Cahn equation on a two-dimensional lattice ⋮ Nontrivial large-time behaviour in bistable reaction-diffusion equations ⋮ Sharp large time behaviour in \(N\)-dimensional reaction-diffusion equations of bistable type ⋮ Localized and expanding entire solutions of reaction-diffusion equations

Cites Work

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• Spherically symmetric solutions of a reaction-diffusion equation
• Asymptotic behaviour of a reaction-diffusion equation in higher space dimensions
• Semigroups of linear operators and applications to partial differential equations
• Long time behavior of solutions of bistable nonlinear diffusion equations
• Geometric theory of semilinear parabolic equations
• Weighted norms for the stability of traveling waves
• The approach of solutions of nonlinear diffusion equations to travelling front solutions
• Multidimensional nonlinear diffusion arising in population genetics
• Asymptotic behavior of solutions of reaction-diffusion equations with varying drift coefficients
• Multidimensional Stability of Traveling Waves in a Bistable Reaction–Diffusion Equation, I
• Multidimensional Stability of Traveling Waves in a Bistable Reaction–Diffusion Equation, II
• Multidimensional stability of planar travelling waves

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