Complete Radiation Conditions for Curved and Elastic Boundaries

Definitions and mathematical statement

Here CRBC abbreviates complete radiation boundary condition; the CRBC method is the method referred to in the supplied source record. Neither its defining equations nor its corner treatment are specified in that record.

Source question. Can the complete radiation boundary condition method be adapted to CRBC corner treatments, extended from corners to smooth boundaries, and applied to more complicated hyperbolic systems, including elasticity, with a rigorous mathematical analysis?

This is a research question whose precise mathematical formulation remains incomplete. The record supplies no particular hyperbolic equation or system, spatial dimension, domain, boundary regularity class beyond the word "smooth," initial or boundary data, material assumptions for elasticity, or defining equations for the proposed boundary conditions. It also does not specify the conclusions that a rigorous analysis must establish. Consequently, no uniquely determined quantified existence, stability, error, or convergence statement can be extracted without additional source information. These are unresolved qualifications, rather than additional hypotheses imposed on the question.

Short English statement

The question asks for extensions of the CRBC method involving corner treatments, smooth boundaries, and more complicated hyperbolic systems such as elasticity, together with rigorous analysis. The supplied record leaves the equations, hypotheses, construction, and required analytical conclusions unspecified, so this remains a qualified research question.

Sources

• Local registry: data/unsolvedmath/problems.json, with catalog/problems.json as the supplementary registry; supplied permanent catalogue entry, source problem code catalogue entry. Collection: Oberwolfach Reports Open Problems. These are registry references supplied for this draft, not independently inspected files.
• Supplied source citation: Computational Electromagnetism and Acoustics (2010), Oberwolfach Reports, DOI 10.4171/owr/2010/10, pp. 415--519. https://doi.org/10.4171/owr/2010/10. The supplied literature-source list labels this same reference "Oberwolfach Report 10/2010." The background describes Oberwolfach Reports as documenting mathematical workshops and their open-problem discussions. The proposed year is 2010; no individual proposer is identified.
• Supplied source-verification qualification: the record labels the statement "exact" and reports that its mathematical content was checked against the official report, with notation, context, and question form normalized without changing the source-level claim. This verification claim is supplied metadata and has not been independently verified here.
• Supplied dated literature curation, checked 2026-08-21: the record labels the problem open and states that CRBC methods have been analyzed for important polygonal and standard wave settings, but that no source found in that curation supplies the requested general extension to curved smooth boundaries, elasticity, and a complete rigorous analysis. This is supplied dated curation derived from the OWR record, not an independently verified literature assessment. The source expressly calls for independent verification of time-sensitive status and cited claims.