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math.AP2026
The unified transform for Burgers' equation: Application to unsaturated flow in finite interval
Konstantinos Kalimeris, Leonidas Mindrinos, Athanasios Paraskevopoulos
In this paper, we focus on one-dimensional vertical infiltration, assuming constant diffusivity and a quadratic relationship between hydraulic conductivity and water content. Under…
math.AP2025
Estimating parameters of the diffusion model via asymptotic expansions
Konstantinos Kalimeris, Leonidas Mindrinos
A broad class of inverse problems deals with determining certain parameters, from measurement data, in models which are associated to certain partial differential equations. In thi…