21 citations · 25 across the 8 of their papers we have counts for
11 papers
A backward problem for the time-fractional pseudo-parabolic equation with a variable coefficient
Arshyn Altybay
This work addresses an inverse reconstruction task for a time-fractional pseudo-parabolic model with a temporally varying coefficient. By imposing Dirichlet boundary conditions, we…
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 dependent coefficients. For bounded measurable…
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 nonsmooth initial--boundary data. When the diffusion, drift, or potential terms, as well…
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…
Numerical identification of the time-dependent coefficient in the heat equation with fractional Laplacian
Arshyn Altybay, Gulzat Nalzhupbayeva
We consider the inverse problem of identifying a time-dependent source coefficient in a one-dimensional heat equation governed by the spectral Dirichlet fractional Laplacian from a…
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…
Numerical Identification of a Time-Dependent Coefficient in a Time-Fractional Diffusion Equation with Integral Constraints
Arshyn Altybay
In this paper, we numerically address the inverse problem of identifying a time-dependent coefficient in the time-fractional diffusion equation. An a priori estimate is established…
A parallel hybrid implementation of the 2D acoustic wave equation
Arshyn Altybay, Michael Ruzhansky, Niyaz Tokmagambetov
In this paper, we propose a hybrid parallel programming approach for a numerical solution of a two-dimensional acoustic wave equation using an implicit difference scheme for a sing…
Tsunami propagation for singular topographies
Arshyn Altybay, Michael Ruzhansky, Mohammed Elamine Sebih +1
We consider a tsunami wave equation with singular coefficients and prove that it has a very weak solution. Moreover, we show the uniqueness results and consistency theorem of the v…
The heat equation with strongly singular potentials
Arshyn Altybay, Michael Ruzhansky, Mohammed Elamine Sebih +1
In this paper, we consider the heat equation with strongly singular potentials and prove that it has a "very weak solution". Moreover, we show the uniqueness and consistency result…
Fractional Schrödinger Equation with singular potentials of higher-order
Arshyn Altybay, Michael Ruzhansky, Mohammed Elamine Sebih +1
In this paper, the space-fractional Schrödinger equations with singular potentials are studied. Delta-like or even higher-order singularities are allowed. By using the regularising…