A Study of Weakly Discontinuous Solutions for Hyperbolic Differential Equations Based on Wavelet Transform Methods

Abstract

A new approach to prove the one-dimensional Cauchy problem's weakly discontinuous solutions for hyperbolic PDEs are on the characteristics is discussed in this paper. To do so, I use wavelet singularity detection methods or WTMM [1] based on two-dimensional wavelet transform and combine it with the Lipschitz index to strengthen the detection.

arXiv comment9 pages, 2 figures, SIAM 2013 Annual Meeting, to appear in Int. J. Appl. Math. arXiv admin note: substantial text overlap with arXiv:1309.5403