The Numerical Solution of an Inverse Pseudoparabolic Problem with a Boundary Integral Observation
Year: 2025
Type: article
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.
Source: Mathematics
DOI: 10.3390/math13060908
Authors: Miglena N. Koleva, Lubin G. Vulkov
Institution: Angel Kanchev University of Ruse
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4408290166