A STUDY OF WEAKLY DISCONTINUOUS SOLUTIONS FOR
HYPERBOLIC DIFFERENTIAL EQUATIONS BASED
ON WAVELET TRANSFORM METHODS
Shijie Gu
Department of Mathematics & Statistics
University of Nevada, Reno
1664 N. Virginia Street
Reno, 89503, USA
Abstract. In this paper, a new approach to prove the one-dimensional Cauchy problem's weakly discontinuous solutions for hyperbolic PDEs on the characteristics is discussed. To do so, we use wavelet singularity detection methods or wavelet transform modulus maxima (WTMM), see [6], based on two-dimensional wavelet transform and combine it with the Lipschitz index to strengthen the detection.
AMS Subject classification: 65T60, 49K20, 65M99
Keywords and phrases: wavelet singularity detection, wavelet transform modulus maxima (WTMM), Lipschitz index


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DOI: 10.12732/ijam.v27i1.1

Volume: 27
Issue: 1
Year: 2014