Fractional Klein-Gordon equation with singular mass
Altybay A. Ruzhansky M. Sebih M.E. Tokmagambetov N.
February 2021Elsevier Ltd
Chaos, Solitons and Fractals
2021#143
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.
Cauchy problem , Fractional wave equation , Numerical analysis , Regularisation , Singular mass , Very weak solution , Weak solution
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Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Belgium
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
School of Mathematical Sciences, Queen Mary University of London, United Kingdom
Laboratory of Analysis and Control of Partial Differential Equations, Djillali Liabes University, Sidi Bel Abbes, Algeria
Laboratory of Geomatics, Ecology and Environment, University Mustapha Stambouli of Mascara, Algeria
Al-Farabi Kazakh National University, Almaty, Kazakhstan
Department of Mathematics: Analysis
Institute of Mathematics and Mathematical Modeling
School of Mathematical Sciences
Laboratory of Analysis and Control of Partial Differential Equations
Laboratory of Geomatics
Al-Farabi Kazakh National University
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