Inverse source problems for time-fractional nonlinear pseudoparabolic equations with p-Laplacian

Khompysh K. Ruzhansky M.
June 2025 Springer Nature

Fractional Calculus and Applied Analysis
2025 #28 Issue 3 1353 - 1383 pp.

In this paper, we deal with a time dependent inverse source problem for a nonlinear p-Laplacian pseudoparabolic equation containing a fractional derivative in time of order α∈(0,1). Moreover, the equation is perturbed by a power-law damping (reaction) term, which, depending on whether its sign is positive or negative, may account for the presence of a source or an absorption within the system. The equation is supplemented with a measurement in a form of an integral over space domain along with the initial and Dirichlet boundary conditions, to determine both the solution of the equation and the unknown source term. For the associated inverse source problem, under suitable assumptions on the data, we establish global and local in time existence and uniqueness of weak solutions for different values of exponents and coefficients.

Fractional derivative , Global and local existence and uniqueness , Inverse problem , P-Laplacian and damping , Pseudoparabolic equations , Weak solutions

Text of the article Перейти на текст статьи

Al-Farabi Kazakh National University, Almaty, Kazakhstan
Ghent University, Ghent, Belgium
Queen Mary University of London, London, United Kingdom

Al-Farabi Kazakh National University
Ghent University
Queen Mary University of London

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026