Inverse norm estimation of perturbed Laplace operators and corresponding eigenvalue problems
Numerical Analysis
2021-12-15 v2 Numerical Analysis
Analysis of PDEs
Functional Analysis
Spectral Theory
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-Lehman-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.
Cite
@article{arxiv.1910.02200,
title = {Inverse norm estimation of perturbed Laplace operators and corresponding eigenvalue problems},
author = {Kouta Sekine and Kazuaki Tanaka and Shin'ichi Oishi},
journal= {arXiv preprint arXiv:1910.02200},
year = {2021}
}
Comments
14 page, 1 figure