Generation and Propagation of Interfaces in Reaction-Diffusion Systems
From MaRDI portal
Publication:4032482
DOI10.2307/2154487zbMath0785.35006OpenAlexW4234654145MaRDI QIDQ4032482
Publication date: 1 April 1993
Full work available at URL: https://doi.org/10.2307/2154487
asymptotic behaviorfree boundary problemlocal existencesecond initial-boundary value problemgeneration of interfacepropagation of interfacereaction- diffusion system
Asymptotic behavior of solutions to PDEs (35B40) Singular perturbations in context of PDEs (35B25) Free boundary problems for PDEs (35R35) Initial value problems for second-order parabolic systems (35K45)
Related Items
A Harnack inequality for the parabolic Allen-Cahn equation, A phase field approach in the numerical study of the elastic bending energy for vesicle membranes, Asymptotic behavior of solutions of an allen-cahn equation with a nonlocal term, Global existence and uniqueness of solutions for one-dimensional reaction-interface systems, Whole cell tracking through the optimal control of geometric evolution laws, Mean curvature interface limit from Glauber+Zero-range interacting particles, Generation and Motion of Interfaces in a Mass-Conserving Reaction-Diffusion System, Traveling spots on multi-dimensional excitable media, Singular limits of reaction diffusion equations and geometric flows with discontinuous velocity, Traveling Curved Waves in Two-Dimensional Excitable Media, Effects on global coupling of an interface problem in an activator-inhibitor system., The singular limit of the Allen-Cahn equation and the FitzHugh-Nagumo system, Very slow dynamics for some reaction-diffusion systems of the activator- inhibitor type, Layer dynamics for the one dimensional \(\varepsilon\)-dependent Cahn-Hilliard/Allen-Cahn equation, Local existence and uniqueness of solutions of the Stefan problem with surface tension and kinetic undercooling, A Hopf bifurcation in a free boundary problem with inhomogeneous media, A wildland fire model with data assimilation, Internal layers in high-dimensional domains, Generation, propagation, and annihilation of metastable patterns, Generation, motion and thickness of transition layers for a nonlocal Allen-Cahn equation, A hyperbolic-elliptic-parabolic PDE model describing chemotactic \textit{E. coli} colonies, Learning phase field mean curvature flows with neural networks, Type-0 singularities in the network flow -- evolution of trees, Global Dynamics on One-Dimensional Excitable Media, A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Classes of solutions of linear systems of partial differential equations of parabolic type
- Motion of level sets by mean curvature. I
- Higher-dimensional localized patterns in excitable media
- Curvature and the evolution of fronts
- Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
- Dynamics of interfaces in reaction diffusion systems
- Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics
- Generation and propagation of interfaces for reaction-diffusion equations
- The approach of solutions of nonlinear diffusion equations to travelling front solutions
- Multidimensional nonlinear diffusion arising in population genetics
- Slow-motion manifolds, dormant instability, and singular perturbations
- Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations
- Fast Reaction, Slow Diffusion, and Curve Shortening
- Invariant manifolds for metastable patterns in ut = ε2uxx—f(u)
- On the slowness of phase boundary motion in one space dimension
- A free boundary problem arising in some reacting–diffusing system
- Global Existence of Weak Solutions for Interface Equations Coupled with Diffusion Equations
- Phase transitions and generalized motion by mean curvature
- The generation and propagation of internal layers
- Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
