Computer-assisted proofs for radially symmetric solutions of PDEs

DOI10.3934/JCD.2018003zbMath1409.35017OpenAlexW2896220636MaRDI QIDQ1728241

Xianqiang Yang

Publication date: 22 February 2019

Published in: Journal of Computational Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/jcd.2018003

zbMATH Keywords

Taylor seriescontraction mapping theoremgeometric elliptic PDEs on manifolds

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) General methods in interval analysis (65G40) Theoretical approximation in context of PDEs (35A35) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Algorithms with automatic result verification (65G20) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Implicit function theorems; global Newton methods on manifolds (58C15) Semilinear elliptic equations (35J61)

Related Items (12)

Rotation invariant patterns for a nonlinear Laplace-Beltrami equation: a Taylor-Chebyshev series approach ⋮ A rigorous implicit \(C^1\) Chebyshev integrator for delay equations ⋮ Constructive proofs for localised radial solutions of semilinear elliptic systems on Rd ⋮ Unstable Stokes waves ⋮ A functional analytic approach to validated numerics for eigenvalues of delay equations ⋮ Computer-assisted estimates for Birkhoff normal forms ⋮ Validated numerical solutions for a semilinear elliptic equation on some topological annuli in the plane ⋮ Computer-assisted proofs for radially symmetric solutions of PDEs ⋮ Parameterization Method for Unstable Manifolds of Standing Waves on the Line ⋮ Spatial relative equilibria and periodic solutions of the Coulomb \((n+1)\)-body problem ⋮ An Asymptotic Analysis of Localized Three-Dimensional Spot Patterns for the Gierer--Meinhardt Model: Existence, Linear Stability, and Slow Dynamics ⋮ Free Vibrations in a Wave Equation Modeling MEMS

Uses Software

• Matlab
• INTLAB
• CAPD
• RODES

Cites Work

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