finite-difference methods 1inverse problems 1pseudo-parabolic equations 1regularization 1time-fractional PDEs 1variable coefficients 1
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math.AP2026
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…
math.AP2026
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…
math.AP2026
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…