Fractional Klein-Gordon equation with singular mass

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 ${\delta }^2$ is observed.

arXiv comment9 pages, 6 figures

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Cited by in corpus (4)

• The heat equation with strongly singular potentials
• Stochastic parabolic equations with singular potentials
• Fractional Klein-Gordon equation with singular mass. II: Hypoelliptic case
• Fractional Schrödinger equations with singular potentials of higher order. II: Hypoelliptic case