5 papers
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…
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…
Low-Regularity Solutions of the Nonlinear Schrödinger Equation on the Spatial Quarter-Plane
Dionyssios Mantzavinos, Türker Ozsarı
The Hadamard well-posedness of the nonlinear Schrödinger equation with power nonlinearity formulated on the spatial quarter-plane is established in a low-regularity setting with S…
The complex Ginzburg-Landau equation on a finite interval and chaos suppression via a finite-dimensional boundary feedback stabilizer
Dionyssios Mantzavinos, Türker Ãzsarı, Kemal Cem Yılmaz
In this paper, we study the well-posedness and boundary stabilization of the initial-boundary value problem for the complex Ginzburg-Landau (CGL) equation on a finite interval. Fir…
Stabilization of linear waves with inhomogeneous Neumann boundary conditions
Türker Ãzsarı, Ä°dem Susuzlu
We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary conditio…