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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Weak solutions with unbounded variation


Author: Donald P. Ballou
Journal: Proc. Amer. Math. Soc. 37 (1973), 181-184
MSC: Primary 35L60
DOI: https://doi.org/10.1090/S0002-9939-1973-0328367-7
MathSciNet review: 0328367
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Abstract: To solve a quasilinear system of hyperbolic partial differential equations with given initial data, the usual procedure is to approximate the initial data, solve the resulting problems, and show that the variation of the approximating solutions is uniformly bounded. A limiting process then can be used. This paper shows that, for simple systems, the variation of the solution need not be finite.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0328367-7
Keywords: Weak solutions, quasilinear hyperbolic systems, initial value problems, unbounded variation
Article copyright: © Copyright 1973 American Mathematical Society