Name
Title | ||
|---|---|---|
Inverse norm estimation of perturbed Laplace operators and corresponding eigenvalue problems |
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. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1016/j.camwa.2021.12.002 | COMPUTERS & MATHEMATICS WITH APPLICATIONS |
Keywords | DocType | Volume |
Eigenvalue evaluation, System of partial differential equations, Norm of inverse operators, Rigorous numerical computations, Computer-assisted proofs | Journal | 106 |
ISSN | Citations | PageRank |
0898-1221 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kouta Sekine | 1 | 0 | 1.69 |
| Tanaka Kazuaki | 2 | 0 | 0.34 |
| Shin'ichi Oishi | 3 | 280 | 37.14 |