5 papers · 1 filter
Backward Behavior and Determining Functionals for Chevron Pattern Equations
Varga K. Kalantarov, Habiba V. Kalantarova, Orestis Vantzos
The paper is devoted to the study of the backward behavior of solutions of the initial boundary value problem for the chevron pattern equations under homogeneous Dirichlet's bounda…
Grain Boundary Grooving in a Bicrystal with Passivation Coating
H. Kalantarova, L. Klinger, E. Rabkin
We use the sixth order linear parabolic equation \begin{equation} \frac{\partial y}{\partial t}=B\left(α\frac{\partial^{6}y}{\partial x^{6}}-\frac{\partial^{4}y}{\partial x^{4}}\ri…
Chevron pattern equations: exponential attractor and global stabilization
H. Kalantarova, V. Kalantarov, O. Vantzos
The initial boundary value problem for a nonlinear system of equations modeling the chevron patterns is studied in one and two spatial dimensions. The existence of an exponential a…
Global Behavior of Solutions to Chevron Pattern Equations
H. Kalantarova, V. Kalantarov, O. Vantzos
Considering a system of equations modeling the chevron pattern dynamics, we show that the corresponding initial boundary value problem has a unique weak solution that continuously…
Self-Similar Grooving Solutions to the Mullins' Equation
Habiba Kalantarova, Amy Novick-Cohen
In 1957, Mullins proposed surface diffusion motion as a model for thermal grooving. By adopting a small slope approximation, he reduced the model to the Mullins' linear surface dif…