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| Content Provider | Springer Nature Link |
|---|---|
| Author | Nicholls, David P. Taber, Mark |
| Copyright Year | 2007 |
| Abstract | In this paper we take up the question of analyticity properties of Dirichlet–Neumann operators (DNO) which arise in boundary value and free boundary problems from a wide variety of applications (e.g., fluid and solid mechanics, electromagnetic and acoustic scattering). More specifically, we consider DNO defined on domains inspired by the simulation of ocean waves over bathymetry, i.e. domains perturbed independently at both the top and bottom. Our analysis shows that the DNO, when perturbed from an arbitrary smooth domain, is parametrically analytic (as a function of deformation height/slope) for profiles of finite smoothness. Additionally, we extend these results to joint spatial and parametric analyticity when the perturbations are real analytic. This analysis is novel not only in that it accounts for the doubly perturbed nature of the geometry, but also in that the technique of proof establishes the full joint analyticity from an arbitrary smooth profile simultaneously. |
| Ending Page | 271 |
| Page Count | 34 |
| Starting Page | 238 |
| File Format | |
| ISSN | 14226928 |
| e-ISSN | 14226952 |
| Journal | Journal of Mathematical Fluid Mechanics |
| Issue Number | 2 |
| Volume Number | 10 |
| Language | English |
| Publisher | SP Birkhäuser Verlag Basel |
| Publisher Date | 2007-02-26 |
| Publisher Place | Basel |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | boundary perturbation methods Dirichlet–Neumann operators geometric perturbation PDEs in connection with fluid mechanics water waves Free-surface potential flows Water waves, gravity waves; dispersion and scattering, nonlinear interaction Mechanics, Fluids, Thermodynamics Mathematical Methods in Physics Fluids Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation free-boundary problems boundary value problems |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Mathematical Physics Condensed Matter Physics Computational Mathematics |
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