9780821825730 / 0821825739

Ondes De Gradients Multidimensionnelles (Memoirs of the American Mathematical Society)


Publisher:Amer Mathematical Society, 1993



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About the book:

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.

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