Inverse norm estimation of perturbed Laplace operators and corresponding eigenvalue problems
arXiv:1910.02200 · doi:10.1016/j.camwa.2021.12.002
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.
14 page, 1 figure