Critical spectrum and stability of interfaces for a class of reaction-diffusion equations

DOI10.1006/jdeq.1996.0046zbMath0879.35074OpenAlexW1984271344MaRDI QIDQ1912515

Nicholas D. Alikakos, Giorgio Fusco, Vangelis Stefanopoulos

Publication date: 18 January 1998

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

Full work available at URL: https://doi.org/10.1006/jdeq.1996.0046

zbMATH Keywords

Allen-Cahn equation

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Stability of manifolds of solutions to ordinary differential equations (34D35)

Related Items (18)

Semilinear Neumann boundary value problems on a rectangle ⋮ Exponentially slow dynamics and interfaces intersecting the boundary ⋮ On positive solutions generated by semi-strong saturation effect for the Gierer-Meinhardt system ⋮ A center manifold analysis for the Mullins-Sekerka model ⋮ Global dynamics of boundary droplets ⋮ Singular perturbation and bifurcation of diffuse transition layers in inhomogeneous media. II ⋮ Global existence and full convergence of the Möbius-invariant Willmore flow in the 3-sphere ⋮ Rotationally symmetric solutions to the Cahn-Hilliard equation ⋮ Moduli space theory for the Allen-Cahn equation in the plane ⋮ Mesa-type patterns in the one-dimensional Brusselator and their stability ⋮ Slow travelling waves on a finite interval for Burgers'-type equations ⋮ Internal layers intersecting the boundary of domain in the Allen-Cahn equation ⋮ Slow dynamics in reaction–diffusion systems ⋮ Nondegeneracy and the Jacobi fields of rotationally symmetric solutions to the Cahn-Hillard equation ⋮ Characterization of hypersurfaces via the second eigenvalue of the Jacobi operator ⋮ Multiple-end solutions to the Allen-Cahn equation in \(\mathbb R^2\) ⋮ Variational aspects of phase transitions with prescribed mean curvature ⋮ The ground state of a Gross-Pitaevskii energy with general potential in the Thomas-Fermi limit

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