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On corner irregularities that arise in hyperbolic shell membrane theory
Author(s) -
Piila J.,
Pitkäranta J.
Publication year - 2002
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.316
Subject(s) - mathematics , singularity , domain (mathematical analysis) , mathematical analysis , algebraic number , gravitational singularity , point (geometry) , focus (optics) , pure mathematics , geometry , physics , optics
We study the regularity of the solution to a two‐dimensional linear hyperbolic system that arises in shell membrane theory. We focus on the behaviour of the solution at a corner where none of the characteristic lines intersect the domain. In this case, there appears an algebraic singularity at the corner, in addition to the usual hyperbolic irregularities that propagate along the characteristic lines. We carry out the analysis on a triangular domain, using as tools the Banach fixed point Theorem and the Mellin transform techniques. Copyright © 2002 John Wiley & Sons, Ltd.