4 research outputs found
Improved Reduced Order Mechanical Model and Finite Element Analysis of Three-Dimensional Deformations of Epithelial Tissues
In this chapter, we analyse non-uniform bending of single-layer cell tissues—epithelia, surrounding organs throughout the body. Dimensionally reduced model is suggested, which is equivalent to membranes with bending stiffness: the total elastic energy of the tissue is a combination of stretching and bending energies. The energy, suggested in this chapter, is a piecewise function, the branches of which correspond to a specific deformation regime: compression, pure bending and stretch
Exact and approximate distributed controllability of processes described by KdV and Boussinesq equations: The Green’s function approach
In this paper, we study the constrained exact and approximate controllability of traveling
wave solutions of Korteweg-de Vries (third order) and Boussinesq (fourth order) semi-linear
equations using the Green’s function approach. Control is carried out by a moving external
source. Representing the general solution of those equations in terms of the Frasca’s short
time expansion, system of constraints on the distributed control is derived for both types of
controllability. Due to the possibility of explicit solution provided by the heuristic method,
the controllability analysis becomes straightforward. Numerical analysis confirms theoretical
derivations