DETERMINING SOURCES PROBLEM IN A PSEUDOPARABOLIC EQUATION OF THE THIRD ORDER
DETERMINING SOURCES PROBLEM IN A PSEUDOPARABOLIC EQUATION OF THE THIRD ORDER
DOI:
https://doi.org/10.52754/16948645_2023_2_104Keywords:
inverse problem, pseudoparabolic equation of the third order, resolvent, Volterra integral equation of the second kind, Green's functionAbstract
In this paper, the inverse source problem for a class of third-order pseudo-parabolic equations with variable coefficients is investigated. The right part is the sum of several spatially localized sources whose intensities change over time and are unknown. As additional information, the temperature values at some points are set as a function of time. Using the Green function of a mixed boundary value problem for second-order ordinary differential equations with variable coefficients, as well as the resolvent method and the Green function method, the conditions for the existence and uniqueness of the solution of the inverse problem are found.
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