Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

A radiation-conditioned Gaussian induced MGD conefield


Author: Lim Chee-seng
Journal: Quart. Appl. Math. 35 (1977), 321-335
DOI: https://doi.org/10.1090/qam/99644
MathSciNet review: QAM99644
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Abstract: Explicit radiation-conditioned solutions are derived for magnetically-aligned MGD flow past a Gaussian source. If the latter's principal dimension is small, then corresponding to a supersonic-superAlfvénic (or restricted subsonic-subAlfvénic) flow, a strong perturbation field is encountered downstream from a downstream (or upstream from an upstream) tangent cone to the ``fast'' sheet (or one of the two ``slow'' cusped sheets) of the Friedrichs wavefront, while a weak estimable field appears upstream (or downstream) from this cone. The strong field is represented by an expansion with accessible asymptotic development. For a finite principal source dimension, other asymptotic modes can be extracted from a separate uniformly valid formulation. In particular, the asymptotic behavior near the dividing tangent cone is nonsingular and suggests the possible existence there of a conical sheath within which the field is probably most concentrated, and across which its transition from strong to weak occurs gradually.


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DOI: https://doi.org/10.1090/qam/99644
Article copyright: © Copyright 1977 American Mathematical Society


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