Layered solutions with multiple asymptotes for non autonomous Allen-Cahn equations in \({\mathbb {R}^{3}}\)

DOI10.1007/s00526-012-0495-2zbMath1266.35075OpenAlexW2047956630MaRDI QIDQ1942235

Francesca Alessio, Piero Montecchiari

Publication date: 18 March 2013

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-012-0495-2

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Variational methods for second-order elliptic equations (35J20) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Semilinear elliptic equations (35J61)

Related Items (11)

Existence of a heteroclinic solution for a double well potential equation in an infinite cylinder of $\mathbb{R}^{N}$ ⋮ The heteroclinic connection problem for general double-well potentials ⋮ Saddle solutions for bistable symmetric semilinear elliptic equations ⋮ Gradient Lagrangian systems and semilinear PDE ⋮ Complex dynamics in a ODE model related to phase transition ⋮ Existence of heteroclinic and saddle-type solutions for a class of quasilinear problems in whole ℝ2 ⋮ Existence of saddle-type solutions for a class of quasilinear problems in \(\mathbb{R}^2\) ⋮ Layered solutions for a nonlocal Ginzburg-Landau model with periodic modulation ⋮ Multiplicity of layered solutions for Allen-Cahn systems with symmetric double well potential ⋮ On the existence of dark solitons of the defocusing cubic nonlinear Schrödinger equation with periodic inhomogeneous nonlinearity ⋮ Brake orbit solutions for semilinear elliptic systems with asymmetric double well potential

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Extensions of Moser-Bangert theory. Locally minimal solutions
• The space of 4-ended solutions to the Allen-Cahn equation in the plane
• Perturbation methods and semilinear elliptic problems on \(\mathbb R^n\)
• Saddle-shaped solutions of bistable diffusion equations in all of \(\mathbb R^{2m}\)
• Slope-changing solutions of elliptic problems on \(\mathbb R^n\)
• Entire solutions of autonomous equations on \(\mathbb{R}^n\) with nontrivial asymptotics
• Saddle-type solutions for a class of semilinear elliptic equations
• The Toda system and multiple-end solutions of autonomous planar elliptic problems
• Some new entire solutions of semilinear elliptic equations on \(\mathbb R^n\)
• Multiple-end solutions to the Allen-Cahn equation in \(\mathbb R^2\)
• Minimal solutions of variational problems on a torus
• On minimal laminations of the torus
• Saddle solutions of the bistable diffusion equation
• On a conjecture of De Giorgi and some related problems
• Multiple solutions to a Dirichlet problem on bounded symmetric domains
• Stationary layered solutions in \(\mathbb{R}^ 2\) for an Allen-Cahn system with multiple well potential
• Homoclinics: Poincaré-Melnikov type results via a variational approach
• One-dimensional symmetry of bounded entire solutions of some elliptic equations
• Stationary layered solutions in \(\mathbb{R}^2\) for a class of non autonomous Allen-Cahn equations
• Elliptic partial differential equations of second order
• Symmetry for solutions of semilinear elliptic equations in \(\mathbb{R}^N\) and related conjectures
• Mixed states for an Allen-Cahn type equation. II
• On some results of Moser and of Bangert
• A counterexample to a conjecture by De Giorgi in large dimensions
• Multiplicity results for interfaces of Ginzburg-Landau-Allen-Cahn equations in periodic media
• Regularity of flat level sets in phase transitions
• On the necessity of gaps
• Brake orbits type solutions to some class of semilinear elliptic equations
• Qualitative Properties of Saddle-Shaped Solutions to Bistable Diffusion Equations
• $1$D symmetry for solutions of semilinear and quasilinear elliptic equations
• Nondegeneracy of the saddle solution of the Allen-Cahn equation
• EXISTENCE OF INFINITELY MANY STATIONARY LAYERED SOLUTIONS INR²FOR A CLASS OF PERIODIC ALLEN–CAHN EQUATIONS
• Some results on minimizers and stable solutions of a variational problem
• Entire solutions in ${\mathbb{R}}^{2}$ for a class of Allen-Cahn equations
• Multiplicity of Entire Solutions For a Class of Almost Periodic Allen-Cahn Type Equations
• Bernstein and De Giorgi type problems: new results via a geometric approach
• Symmetric quadruple phase transitions
• Uniqueness of positive radial solutions of semilinear elliptic equations in R^Nand séré's non—degeneracy condition
• Asymmetric heteroclinic double layers
• Mixed states for an Allen‐Cahn type equation
• Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
• On Some Results of Moser and of Bangert, II
• On the stability of the saddle solution of Allen–Cahn's equation
• On De Giorgi’s conjecture and beyond
• Genericity of the multibump dynamics for almost periodic Duffing-like systems
• Many Solutions of Elliptic Problems on Rⁿof Irrational Slope
• On a long-standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property

This page was built for publication: Layered solutions with multiple asymptotes for non autonomous Allen-Cahn equations in \({\mathbb {R}^{3}}\)