2012/10/28 by Constantin N. Beli, Beli, Constantin N., Liviu I. Ignat +3
Earth and Planetary Sciences · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.1210.7415
openalex publication_date 2012/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we analyze the dispersion for one dimensional wave and Schrodinger equations with BV coefficients. In the case of the wave equation we give a complete answer in terms of the variation of the logarithm of the coefficient showing that dispersion occurs if this variation is small enough but it may fail when the variation goes beyond a sharp threshold. For the Schrodigner equation we prove that the dispersion holds under the same smallness assumption on the variation of the coefficient. But, whether dispersion may fail for larger coefficients is unknown for the Schrodinger equation.