Abstract
We investigate the operator-norm resolvent asymptotics of a high-contrast composite, consisting of a “stiff” material, with annular “soft” inclusions (a “stiff-soft-stiff” setup). This setup is derived from two models with very different effective wave propagation behaviours. Our analysis is based on an operator-framework proposed by Cherednichenko, Ershova, and Kiselev in [15]. Then, as a first step towards studying wave propagation on the stiff-soft-stiff composite, we use the effective description to derive analogous “dispersion functions”.
| Original language | English |
|---|---|
| Article number | 128462 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 539 |
| Issue number | 1 (Part1) |
| Early online date | 29 Apr 2024 |
| DOIs | |
| Publication status | Published - 1 Nov 2024 |
Data Availability Statement
No new data were created during this study.Funding
YSL is supported by a scholarship from the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa), under the project EP/S022945/1. YSL would like to thank to Prof. Kirill D. Cherednichenko for his patience, guidance, and the many helpful discussions throughout this project. YSL would like to thank Dr. Alexander V. Kiselev, Prof. Euan Spence, and Prof. David Krej\u010Di\u0159\u00EDk for their careful reading of the manuscript and helpful comments. YSL would like to thank anonymous reviewer for their helpful comments and suggestions.
| Funders | Funder number |
|---|---|
| EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa) | EP/S022945/1 |
Keywords
- Homogenization
- Resolvent asymptotics
- Resonant composites
- Wave propagation
ASJC Scopus subject areas
- Analysis
- Applied Mathematics