The Numerical Solution of an Inverse Pseudoparabolic Problem with a Boundary Integral Observation

Miglena N. Koleva () and Lubin G. Vulkov
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Miglena N. Koleva: Department of Mathematics, Faculty of Natural Sciences and Education, “Angel Kanchev” University of Ruse, 8 Studentska Str., 7017 Ruse, Bulgaria
Lubin G. Vulkov: Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, “Angel Kanchev” University of Ruse, 8 Studentska Str., 7017 Ruse, Bulgaria

Mathematics, 2025, vol. 13, issue 6, 1-19

Abstract: Direct and inverse problems for a pseudoparabolic equation are considered. The direct (forward) problem is to find the solution of the corresponding initial–boundary-value problem for known model parameters, as well as the initial and boundary conditions. The well-posedness of the direct problem is shown and a priori estimates of the solution are obtained. We study the inverse problem for identifying the flux on a part of the boundary of a rectangle, using integral measurement on the same part of the boundary. We first reduce the inverse problem to a direct one. The initial–boundary-value direct problem is with nonclassical (integrodifferential) boundary conditions. We develop a finite-difference scheme for numerically solving this problem. Numerical test examples demonstrate the effectiveness of the proposed method. It successfully handles the nonclassical integrodifferential boundary conditions and provides accurate numerical solutions.

Keywords: pseudoparabolic equation; inverse problem; integral observation; point observation; nonlocal boundary conditions; finite-difference method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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