Reflectionless boundary propagation formulas for partial wave solutions to the wave equation
dimensions whose data is compactly supported at some initial time. For points outside a ball containing the initial support, we develop an outgoing wave condition, and associated one-way propagation formula, for the partial waves in the spherical-harmonic decomposition of the solution. The propagati...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
1995-11-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/1995/17/abstr.html |
| _version_ | 1818824530288705536 |
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| author | Jaime Navarro Henry A. Warchall |
| author_facet | Jaime Navarro Henry A. Warchall |
| author_sort | Jaime Navarro |
| collection | DOAJ |
| description | dimensions whose data is compactly supported at some initial time. For points outside a ball containing the initial support, we develop an outgoing wave condition, and associated one-way propagation formula, for the partial waves in the spherical-harmonic decomposition of the solution. The propagation formula expresses the $l$-th partial wave at time $t$ and radius $a$ in terms of order-$l$ radial derivatives of the partial wave at time $t-Delta t$ and radius $a-Delta t$. The boundary propagation formula can be applied to any differential equation that is well-approximated by the wave equation outside a fixed ball. |
| first_indexed | 2024-12-18T23:57:20Z |
| format | Article |
| id | doaj.art-f6b78901904f457a88b91401d8b3530b |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-18T23:57:20Z |
| publishDate | 1995-11-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-f6b78901904f457a88b91401d8b3530b2022-12-21T20:46:39ZengTexas State UniversityElectronic Journal of Differential Equations1072-66911995-11-01199517114Reflectionless boundary propagation formulas for partial wave solutions to the wave equationJaime NavarroHenry A. Warchalldimensions whose data is compactly supported at some initial time. For points outside a ball containing the initial support, we develop an outgoing wave condition, and associated one-way propagation formula, for the partial waves in the spherical-harmonic decomposition of the solution. The propagation formula expresses the $l$-th partial wave at time $t$ and radius $a$ in terms of order-$l$ radial derivatives of the partial wave at time $t-Delta t$ and radius $a-Delta t$. The boundary propagation formula can be applied to any differential equation that is well-approximated by the wave equation outside a fixed ball.http://ejde.math.txstate.edu/Volumes/1995/17/abstr.htmlOne-sided wave propagationWave equationReflectionless boundary conditionsPartial wavesSpherical-harmonic decompositionOpen-space boundary conditions. |
| spellingShingle | Jaime Navarro Henry A. Warchall Reflectionless boundary propagation formulas for partial wave solutions to the wave equation Electronic Journal of Differential Equations One-sided wave propagation Wave equation Reflectionless boundary conditions Partial waves Spherical-harmonic decomposition Open-space boundary conditions. |
| title | Reflectionless boundary propagation formulas for partial wave solutions to the wave equation |
| title_full | Reflectionless boundary propagation formulas for partial wave solutions to the wave equation |
| title_fullStr | Reflectionless boundary propagation formulas for partial wave solutions to the wave equation |
| title_full_unstemmed | Reflectionless boundary propagation formulas for partial wave solutions to the wave equation |
| title_short | Reflectionless boundary propagation formulas for partial wave solutions to the wave equation |
| title_sort | reflectionless boundary propagation formulas for partial wave solutions to the wave equation |
| topic | One-sided wave propagation Wave equation Reflectionless boundary conditions Partial waves Spherical-harmonic decomposition Open-space boundary conditions. |
| url | http://ejde.math.txstate.edu/Volumes/1995/17/abstr.html |
| work_keys_str_mv | AT jaimenavarro reflectionlessboundarypropagationformulasforpartialwavesolutionstothewaveequation AT henryawarchall reflectionlessboundarypropagationformulasforpartialwavesolutionstothewaveequation |