Fractional Klein-Gordon equation with singular mass

Arshyn Altybay, Michael Ruzhansky, Mohammed Elamine Sebih and Niyaz Tokmagambetov

Chaos, Solitons & Fractals, 2021, vol. 143, issue C

Abstract: We consider a space-fractional wave equation with a singular mass term depending on the position and prove that it is very weak well-posed. The uniqueness is proved in some appropriate sense. Moreover, we prove the consistency of the very weak solution with classical solutions when they exist. In order to study the behaviour of the very weak solution near the singularities of the coefficient, some numerical experiments are conducted where the appearance of a wall effect for the singular masses of the strength of δ2 is observed.

Keywords: Fractional wave equation; Cauchy problem; Weak solution; Singular mass; Very weak solution; Regularisation; Numerical analysis (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:143:y:2021:i:c:s096007792030970x

DOI: 10.1016/j.chaos.2020.110579

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