Fractional wave equation with irregular mass and dissipation

2023/11/02 by Ruzhansky, Michael, Sebih, Mohammed Elamine, Tokmagambetov, Niyaz
#35A35 #35D30 #35L05 #35L81 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.01639

Abstract

In this paper, we pursue our series of papers aiming to show the applicability of the concept of very weak solutions. We consider a wave model with irregular position dependent mass and dissipation terms, in particular, allowing for delta-like coefficients and prove that the problem has a very weak solution. Furthermore, we prove the uniqueness in an appropriate sense and the coherence of the very weak solution concept with classical theory. A special case of the model considered here, is the so-called telegraph equation.

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