Numerical verification for asymmetric solutions of the Hénon equation on bounded domains

@article{Asai2020NumericalVF,
  title={Numerical verification for asymmetric solutions of the H{\'e}non equation on bounded domains},
  author={Taisei Asai and Kazuaki Tanaka and Shin'ichi Oishi},
  journal={J. Comput. Appl. Math.},
  year={2020},
  volume={399},
  pages={113708}
}
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SHOWING 1-10 OF 24 REFERENCES
Bifurcation method for solving multiple positive solutions to Henon equation
Three algorithms based on the bifurcation method are applied to solving the D4 symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a…
kv library
  • 2020
Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations
TLDR
This paper presents a new formulation for the verification of the existence of carboniferous strata, and details the methodology used, as well as some of the techniques used, in this study, to achieve this result.
NON-RADIAL GROUND STATES FOR THE HÉNON EQUATION
We analyse symmetry breaking for ground states of the Henon equation [7] in a ball. Asymptotic estimates of the transition are also given when p is close to either 2 or 2*.
Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
For a given starting point, the sequence of Newton iterates is well known to be invariant under affine transformation of the operator equation to be solved. This property, however, is not…
Verified norm estimation for the inverse of linear elliptic operators using eigenvalue evaluation
This paper proposes a verified numerical method of proving the invertibility of linear elliptic operators. This method also provides a verified norm estimation for the inverse operators. This type of…
Bifurcation method for solving multiple positive solutions to Henon equation on the unit cube
Computer-assisted proofs for semilinear elliptic boundary value problems
For second-order semilinear elliptic boundary value problems on bounded or unbounded domains, a general computer-assisted method for proving the existence of a solution in a “close” and explicit…
Elliptic Problems in Nonsmooth Domains
Foreword Preface 1. Sobolev spaces 2. Regular second-order elliptic boundary value problems 3. Second-order elliptic boundary value problems in convex domains 4. Second-order boundary value problems…
Inclusions and Existence Proofs for Solutions of a Nonlinear Boundary Value Problem by Spectral Numerical Methods
For a specific elliptic boundary value problem with quadratic nonlinearity, we give a partial positive answer to an old conjecture concerning the number of solutions. This result is obtained via an…
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