Well-posedness of heat and wave equations generated by Rubin’s q-difference operator in Sobolev spaces
Shaimardan S. Persson L.-E. Tokmagambetov N.
2023University of Nis
Filomat
2023#37Issue 175799 - 5812 pp.
In this paper, we investigate difference-differential operators of parabolic and hyperbolic types. Namely, we consider non-homogenous heat and wave equations for Rubin’s difference operator. Well-posedness results are obtained in appropriate Sobolev type spaces. In particular, we prove that the heat and wave equations generated by Rubin’s difference operator have unique solutions. We even show that these solutions can be represented by explicit formulas.
A priori estimate , Heat equation, wave equation , q-calculus , q-derivative , q-difference operator , Rubin difference operator , Sobolev type space , Well-posedness
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L. N. Gumilyov, Eurasian National University, 5 Munaytpasov str, Astana, 010008, Kazakhstan
Department of Computer Science and Computational Engineering UiT The Arctic University of Norway, Campus Narvik, Narvik, Norway
Department of computer science and mathematics Karlstad university, Karlstad, Sweden
Centre de Recerca Matemática, Edifici C, Campus Bellaterra, Bellaterra, Barcelona, 08193, Spain
Institute of Mathematics and Mathematical Modeling, 125 Pushkin str, Almaty, 050010, Kazakhstan
L. N. Gumilyov
Department of Computer Science and Computational Engineering UiT The Arctic University of Norway
Department of computer science and mathematics Karlstad university
Centre de Recerca Matemática
Institute of Mathematics and Mathematical Modeling
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