PROC
The existence of a global attractor for a Kuramoto-Sivashinsky type equation in 2D
Aslihan Demirkaya
We consider a variation of the Kuramoto-Sivashinsky Equation in space dimension two. We show that under some assumptions the equation is globally well-posed and posseses a global attractor in the periodic case. The analysis is based on the Lyapunov function approach, point dissipativeness and asymptotic compactness.
keywords: Attractors Kuramoto- Sivashinsky Equation
PROC
Spectral stability analysis for standing waves of a perturbed Klein-Gordon equation
Aslihan Demirkaya Panayotis G. Kevrekidis Milena Stanislavova Atanas Stefanov
In the present work, we introduce a new $\mathcal{PT}$-symmetric variant of the Klein-Gordon field theoretic problem. We identify the standing wave solutions of the proposed class of equations and analyze their stability. In particular, we obtain an explicit frequency condition, somewhat reminiscent of the classical Vakhitov-Kolokolov criterion, which sharply separates the regimes of spectral stability and instability. Our numerical computations corroborate the relevant theoretical result.
keywords: standing waves. linear stability

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