On the asymptotic behavior of symmetric solutions of the Allen-Cahn equation in unbounded domains in \(\mathbb{R}^2\)
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Publication:501463
DOI10.3934/dcds.2017030zbMath1375.35196arXiv1405.1541OpenAlexW2963502135MaRDI QIDQ501463
Cristina Pignotti, Francesco Leonetti, Giorgio Fusco
Publication date: 9 January 2017
Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1405.1541
Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61) Symmetries, invariants, etc. in context of PDEs (35B06) Boundary value problems for second-order elliptic systems (35J57)
Cites Work
- Asymptotic behavior of solutions of semilinear elliptic equations in unbounded domains: two approaches
- Geometric theory of semilinear parabolic equations
- Saddle solutions of the bistable diffusion equation
- On some elementary properties of vector minimizers of the Allen-Cahn energy
- Equivariant entire solutions to the elliptic system \(\Delta u = W_u(u)\) for general \(G\)-invariant potentials
- Asymptotic behavior and rigidity results for symmetric solutions of the elliptic system Δu = W_u(u)
- A uniform estimate for positive solutions of semilinear elliptic equations
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