3 papers
math.AP2026
Fokas method for linear convection-diffusion equation with time-dependent coefficients and its extension to other evolution equations
Konstantinos Kalimeris, Türker Ãzsarı
In this paper, we study a linear convection-diffusion equation with time-dependent coefficients on a bounded interval, motivated by associated physical problems. We apply and adapt…
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.AP2026
A new approach for the analysis of evolution partial differential equations on a finite interval
Türker Ãzsarı, Dionyssios Mantzavinos, Konstantinos Kalimeris
We show that, for certain evolution partial differential equations, the solution on a finite interval can be reconstructed as a superposition of restrictions to $(0,\ell…