Inverse norm estimation of perturbed Laplace operators and corresponding eigenvalue problems

Kouta Sekine*, Kazuaki Tanaka, Shin'ichi Oishi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In numerical existence proofs for solutions of the semi-linear elliptic system, evaluating the norm of the inverse of a perturbed Laplace operator plays an important role. We reveal an eigenvalue problem to design a method for verifying the invertibility of the operator and evaluating the norm of its inverse based on Liu's method and the Temple-Lehmann-Goerisch method. We apply the inverse-norm's estimation to the Dirichlet boundary value problem of the Lotka-Volterra system with diffusion terms and confirm the efficacy of our method.

Original languageEnglish
Pages (from-to)18-26
Number of pages9
JournalComputers and Mathematics with Applications
Volume106
DOIs
Publication statusPublished - 2022 Jan 15

Keywords

  • Computer-assisted proofs
  • Eigenvalue evaluation
  • Norm of inverse operators
  • Rigorous numerical computations
  • System of partial differential equations

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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