Dynamic Boundary Condition
. Viscous boundary, which was first proposed by Lysmer and Kuhlemeyer , is adopted as the boundary condition of the model.
The dynamic boundary condition
ensures that the pressure on the cavity is constant and equal to the vapor pressure.
Two boundary conditions must be imposed on the free surface, namely the kinematic boundary condition and the dynamic boundary condition. The kinematic boundary condition states that the fluid particles on the free surface move always along the surface, i.e.,
The dynamic boundary condition describes the continuity of the stress at the free surface, i.e.,
As an application, we prove the existence of exponential attractors for the reaction-diffusion equation with dynamic boundary condition.
Zhong, "Attractors for parabolic equations with dynamic boundary conditions," Nonlinear Analysis: Theory, Methods & Applications, vol.68, no.6, pp.1723-1732, 2008.
If the sinusoidal pulse was short (close to a single period), it would become compressed in propagation if the dynamic boundary condition
was [sigma](0, t) ~ + sin and stretched if [sigma](0, t) ~ - sin.
We consider the asymptotic behavior of solutions to the following parabolic equations with dynamic boundary conditions
and irregular data,
Differential operators in the solution structures transmit information about the dynamic boundary conditions
from the boundary to the domain.
So, it is necessary to construct a dynamic interval wavelet in solving the PDEs with dynamic boundary conditions
such as the fractional PDEs.
In the interface-tracking methods, the free surface is treated as a boundary of the computational domain, where the kinematic and dynamic boundary conditions