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Memoirs of the American Mathematical Society
1993; 93 pp; softcover
List Price: US$36
Individual Members: US$21.60
Institutional Members: US$28.80
Order Code: MEMO/106/511
Recent techniques in partial differential equations have led to a solution to the general multidimensional Cauchy problem for nonlinear gradient waves. In a blown-up configuration, Sablé-Tougeron constructs a local solution for a quasilinear hyperbolic system with continuous Cauchy data, in which the first derivatives are discontinuous on a hypersurface. This strong singularity is not so problematic as a rarefaction: The use of Alinhac's para-unknown leads to a tame inequality without loss of derivatives for the iterative scheme.
Advanced graduate students studying partial differential equations. Researchers in nonlinear hyperbolic problems.
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