Author

T. Özsarı

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Open access Oct 2026

Stochastic Diffusion Driven by Internal and External Brownian Motions

The purpose of this paper is to introduce a stochastic version of Fokas' unified transform formula for evolution PDEs on domains with boundary. The unified transform method, also known as Fokas method, was originally developed for deterministic initial‐boundary value problems and has, so far, been used primarily in d...

T. Özsarı · Studies in applied mathemati... · 1 citation

Open access Aug 2026

The Fokas method for linear convection–diffusion equation with time-dependent coefficients and its extension to other evolution equations

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 the unified transform method (UTM), also known as the Fokas method, which handles both time-varying coefficients and non-zero boundary da...

Konstantinos Kalimeris, T. Özsarı · Proceedings of the Royal Soc... · 1 citation

Preprint Sep 2026

Local well-posedness of the higher-order nonlinear Schr\"{o}dinger equation on the half-line: the case of two boundary conditions

We prove the local Hadamard well-posedness of the higher-order nonlinear Schr\"odinger equation with negative dispersion coefficient on the half-line under nonzero Dirichlet and Neumann boundary data. The paper uncovers a striking feature of this model: unlike the positive-dispersion case studied in (Alk{\i}n, Mantzavi...

A. Alkin, D. Mantzavinos, T. Özsarı · 1 citation