# A time-dependent inverse source problem for a semilinear pseudo-parabolic equation with Neumann boundary condition

Source: [A time-dependent inverse source problem for a semilinear pseudo-parabolic equation with Neumann boundary condition](<https://www.sota2.com/research/paper/68fa5ced1e209131ce9d585b>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-11-21T05:01:56.111Z

Authors: K. Van Bockstal, K. Khompysh

Published: 2025-02-07T10:47:00.000Z

## Abstract

In this paper, we study the inverse problem for determining an unknown time-dependent source coefficient in a semilinear pseudo-parabolic equation with variable coefficients and Neumann boundary condition. This unknown source term is recovered from the integral measurement over the domain $\\Omega$. Based on Rothe's method, the existence and uniqueness of a weak solution, under suitable assumptions on the data, is established. A numerical time-discrete scheme for the unique weak solution and the unknown source coefficient is designed, and the convergence of the approximations is proven. Numerical experiments are presented to support the theoretical results. Noisy data is handled through polynomial regularisation.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2502.04821>)

[PDF](<https://arxiv.org/pdf/2502.04821.pdf>)