Slow motion for a hyperbolic variation of Allen–Cahn equation in one space dimension

DOI10.1142/S0219891617500011zbMath1391.35028arXiv1510.07168WikidataQ115245217 ScholiaQ115245217MaRDI QIDQ2978139

Raffaele Folino

Publication date: 21 April 2017

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

Full work available at URL: https://arxiv.org/abs/1510.07168

zbMATH Keywords

energy estimatesLyapunov functionmetastabilitydamped nonlinear wave equationtransition layer structure

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Second-order semilinear hyperbolic equations (35L71)

Related Items

Slow motion for one-dimensional nonlinear damped hyperbolic Allen-Cahn systems ⋮ Motion of interfaces for a damped hyperbolic Allen-Cahn equation ⋮ Metastability for nonlinear convection-diffusion equations ⋮ Unnamed Item ⋮ Stability properties and dynamics of solutions to viscous conservation laws with mean curvature operator ⋮ Metastable patterns for a reaction-diffusion model with mean curvature-type diffusion ⋮ Slow motion for a hyperbolic variation of Allen–Cahn equation in one space dimension ⋮ Metastable dynamics for a hyperbolic variant of the mass conserving Allen-Cahn equation in one space dimension ⋮ Metastability and layer dynamics for the hyperbolic relaxation of the Cahn-Hilliard equation ⋮ Semigroup estimates and fast-slow dynamics in parabolic-hyperbolic systems ⋮ Long time dynamics of solutions to \(p\)-Laplacian diffusion problems with bistable reaction terms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Slow motion for gradient systems with equal depth multiple-well potentials
• Generation, propagation, and annihilation of metastable patterns
• Semigroups of linear operators and applications to partial differential equations
• The effect of a singular perturbation on nonconvex variational problems
• Asymptotic behavior and stability of solutions of semilinear diffusion equations
• Slow motion for the Cahn-Hilliard equation in one space dimension
• Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics
• A stochastic model related to the telegrapher's equation
• Metastable patterns for the Cahn-Hilliard equation. I
• Metastable patterns for the Cahn-Hilliard equation. II: Layer dynamics and slow invariant manifold
• Metastable dynamics for hyperbolic variations of the Allen-Cahn equation
• The gradient theory of phase transitions and the minimal interface criterion
• Slow-motion manifolds, dormant instability, and singular perturbations
• Slow motion for equal depth multiple-well gradient systems: the degenerate case
• A Turing model with correlated random walk
• Slow motion of gradient flows
• Analytical and numerical investigation of traveling waves for the Allen–Cahn model with relaxation
• Metastability for Nonlinear Parabolic Equations with Application to Scalar Viscous Conservation Laws
• Slow motion for a hyperbolic variation of Allen–Cahn equation in one space dimension
• Γ-type estimates for the one-dimensional Allen–Cahn’s action
• Hyperbolic travelling fronts
• On the slowness of phase boundary motion in one space dimension
• On the slow dynamics for the Cahn–Hilliard equation in one space dimension
• QUALITATIVE ANALYSIS OF SEMILINEAR CATTANEO EQUATIONS
• Slow Motion in One-Dimensional Cahn–Morral Systems
• Metastable patterns in solutions of u_t = ϵ²u_xx − f(u)
• ON DIFFUSION BY DISCONTINUOUS MOVEMENTS, AND ON THE TELEGRAPH EQUATION
• Slow motion in higher-order systems and \(\Gamma\)-convergence in one space dimension