From the 1 of 7 linked papers with an AI index.
7 papers
A backward problem for the time-fractional pseudo-parabolic equation with a variable coefficient
Arshyn Altybay
The paper studies how to recover the unknown initial condition of a time‑fractional pseudo‑parabolic equation with a time‑dependent coefficient from final‑time data, providing theo…
Heat Equation driven by mixed local-nonlocal operators with non-regular space-dependent coefficients
Arshyn Altybay, Michael Ruzhansky
In this paper, we study the Cauchy problem for a heat equation governed by a mixed local--nonlocal diffusion operator with spatially irregular coefficients. We first establish clas…
Rothe's method in direct and time-dependent inverse source problems for a semilinear pseudo-parabolic equation
Karel Van Bockstal, Khonatbek Khompysh, Arshyn Altybay
In this paper, we investigate the inverse problem of determining an unknown time-dependent source term in a semilinear pseudo-parabolic equation with variable coefficients and a Di…
Parabolic Equations with Singular Coefficients and Boundary Data: Analysis and Numerical Simulations
Arshyn Altybay, Alibek Yeskermessuly
We investigate linear parabolic equations in divergence form with singular coefficients and non-smooth boundary data. When the diffusion, drift, or potential terms, as well as the…
Numerical identification of the time-dependent coefficient in the heat equation with fractional Laplacian
Arshyn Altybay, Niyaz Tokmagambetov, Gulzat Nalzhupbayeva
We address the inverse problem of identifying a time-dependent source coefficient in a one-dimensional heat equation with a fractional Laplacian subject to Dirichlet boundary condi…
Numerical Approaches for Identifying the Time-Dependent Potential Coefficient in the Diffusion Equation
Arshyn Altybay, Michael Ruzhansky
We address the inverse problem of identifying a time-dependent potential coefficient in a one-dimensional diffusion equation subject to Dirichlet boundary conditions and a nonlocal…