Fractional wave equation with irregular mass and dissipation
Ruzhansky M. Sebih M.E. Tokmagambetov N.
October 2024Birkhauser
Zeitschrift fur Angewandte Mathematik und Physik
2024#75Issue 5
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 δ-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.
35A35 , 35D30 , 35L05 , 35L81 , Cauchy problem , Energy method , Position-dependent coefficients , Regularisation , Singular dissipation , Singular mass , Telegraph equation , Very weak solution , Weak solution
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Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, Building S8, Ghent, B 9000, Belgium
School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom
Laboratory of Geomatics, Ecology and Environment (LGEO2E), Mustapha Stambouli University of Mascara, Mascara, 29000, Algeria
Centre de Recerca Matemática, Edifici C, Campus Bellaterra, Bellaterra (Barcelona), 08193, Spain
Institute of Mathematics and Mathematical Modeling, 28 Schevchenko str, Almaty, 050010, Kazakhstan
Department of Mathematics: Analysis
School of Mathematical Sciences
Laboratory of Geomatics
Centre de Recerca Matemática
Institute of Mathematics and Mathematical Modeling
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