Inverse Problem on Finding Unknown Time-Moment for Mixed Wave-Diffusion Equation
Karimov E.T. Tokmagambetov N.E.
July 2024Pleiades Publishing
Lobachevskii Journal of Mathematics
2024#45Issue 73314 - 3322 pp.
Abstract: We targeted a new kind of inverse problem for the wave-diffusion equation. Namely, using the given data we have found not only a solution of the wave-diffusion equation satisfying certain boundary and initial conditions but also an unknown time-moment starting from which the wave process transmitted into the diffusion process. In the practical point of view, even finding the first such time-moment seems very interesting. Our main tool of investigation is a spectral expansion method. In addition, we will use the solution of the corresponding Cauchy problem for differential equation in time-variable.
inverse problem , Mittag-Leffler function , the Cauchy problem , transcendent equation , unknown time-moment , Wave-Diffusion equation
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Fergana State University, Fergana, 150100, Uzbekistan
Romanovskii Institute of Mathematics, Tashkent, 100174, Uzbekistan
Centre de Recerca Matemática, Edifici C, Campus Bellaterra, Barcelona, 08193, Spain
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Fergana State University
Romanovskii Institute of Mathematics
Centre de Recerca Matemática
Institute of Mathematics and Mathematical Modeling
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