Wave equations for the fractional Sturm-Liouville operator with singular coefficients

2023/11/29 by Ruzhansky, Michael, Sebih, Mohammed Elamine, Yeskermessuly, Alibek
#34B24 #35D30 #35L05 #35L20 #35L81 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.17823

Abstract

In this paper, we consider the wave equation for the fractional Sturm-Liouville operator with lower order terms and singular coefficients and data. We prove that the problem has a very weak solution. Furthermore, we prove the uniqueness in an appropriate sense and the consistency of the very weak solution concept with the classical theory.

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