Direct and inverse source problems for heat equation in quantum calculus
Shaimardan S. Ruzhansky M.
2024University of Nis
Filomat
2024#38Issue 238141 - 8156 pp.
In this paper, we explore the weak solutions of the Cauchy problem and an inverse source problem for the heat equation in the quantum calculus, formulated in abstract Hilbert spaces. For this, we use the Fourier series expansions. Moreover, we prove the existence, uniqueness and stability of the weak solution of the inverse problem with a final determination condition. We give some examples such as the q-Sturm–Liouville problem, the q-Bessel operator, the q-deformed Hamiltonian, the fractional Sturm-Liouville operator, and the restricted fractional Laplacian, covered by our analysis.
a priori estimate , Difference operator , heat equation , q-calculus , q-derivative , Sobolev type space , wave equation , well-posedness
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Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
Institute of Mathematics and Mathematical Modeling
Department of Mathematics: Analysis
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