Traveling wave solutions of Allen-Cahn equation with a fractional Laplacian
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Publication:494136
DOI10.1016/j.anihpc.2014.03.005zbMath1326.35068OpenAlexW2050163813MaRDI QIDQ494136
Publication date: 31 August 2015
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.anihpc.2014.03.005
Integral operators (47G10) Variational methods for second-order elliptic equations (35J20) Bifurcations in context of PDEs (35B32) Singular nonlinear integral equations (45G05) Traveling wave solutions (35C07) Fractional partial differential equations (35R11) Integro-partial differential equations (35R09)
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Cites Work
- Local and global minimizers for a variational energy involving a fractional norm
- Density estimates for a variational model driven by the Gagliardo norm
- Traveling waves for a boundary reaction-diffusion equation
- Traveling wave solutions to some reaction diffusion equations with fractional Laplacians
- Uniform estimates and limiting arguments for nonlocal minimal surfaces
- Existence and global stability of traveling curved fronts in the Allen-Cahn equations
- On De Giorgi's conjecture in dimension \(N\geq 9\)
- Asymptotic properties and classification of bistable fronts with Lipschitz level sets
- Global stability of traveling curved fronts in the Allen-Cahn equations
- Energy estimates and 1-D symmetry for nonlinear equations involving the half-Laplacian
- Front-type solutions of fractional Allen-Cahn equation
- The uniqueness and asymptotic stability of pyramidal traveling fronts in the Allen-Cahn equations
- \(\Gamma\) convergence of an energy functional related to the fractional Laplacian
- Front propagation in Fisher-KPP equations with fractional diffusion
- 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
- On a conjecture of De Giorgi and some related problems
- Traveling waves in a convolution model for phase transitions
- On De Giorgi's conjecture in dimensions 4 and 5
- Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations
- Front propagation in reactive systems with anomalous diffusion
- Elliptic partial differential equations of second order
- The speed of propagation for KPP type problems. I: Periodic framework
- Mathematical problems from combustion theory
- Travelling fronts in cylinders
- A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals.
- The gradient theory of phase transitions and the minimal interface criterion
- Metastability and stability of patterns in a convolution model for phase transitions
- Construction of the Leray-Schauder degree for elliptic operators in unbounded domains
- The characterization of reaction-convection-diffusion processes by travelling waves
- Travelling fronts in non-local evolution equations
- Fast propagation for KPP equations with slowly decaying initial conditions
- Existence and asymptotics of fronts in non local combustion models
- Exact solutions in front propagation problems with superdiffusion
- Symmetry of traveling wave solutions to the Allen-Cahn equation in \({\mathbb R^{2}}\)
- Traveling wave solutions in a half-space for boundary reactions
- Regularity of flat level sets in phase transitions
- Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
- Traveling waves with paraboloid like interfaces for balanced bistable dynamics
- A variational model for dislocations in the line tension limit
- Semi-groupes de Feller sur une variété à bord compacte et problèmes aux limites intégro-différentiels du second ordre donnant lieu au principe du maximum
- Heteroclinic solutions of a van der Waals model with infinite nonlocal interactions
- Existence and qualitative properties of multidimensional conical bistable fronts
- Sharp energy estimates for nonlinear fractional diffusion equations
- Heteroclinic travelling waves of gradient diffusion systems
- Nonlocal minimal surfaces
- Multidimensional Stability of Traveling Waves in a Bistable Reaction–Diffusion Equation, I
- Multidimensional Stability of Traveling Waves in a Bistable Reaction–Diffusion Equation, II
- Phase transitions and generalized motion by mean curvature
- Existence of multidimensional travelling waves in the bistable case
- Solutions of Semilinear Elliptic Equations in with Conical&Shaped Level Sets
- Front Propagation in Heterogeneous Media
- Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
- The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
- Front Propagation and Phase Field Theory
- Stability of travelling waves in a model for conical flames in two space dimensions
- On the differentiability of the solution to an equation with drift and fractional diffusion
- $\Gamma$-Limit of a Phase-Field Model of Dislocations
- An Extension Problem Related to the Fractional Laplacian
- Traveling Fronts of Pyramidal Shapes in the Allen–Cahn Equations
- Layer solutions in a half‐space for boundary reactions
- Travelling fronts and entire solutions of the Fisher-KPP equation in \({\mathbb R}^N\)
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
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