In this presentation we investigate the solutions to the reduced plate model, with hinged-free boundary conditions and action of wind in the chord-wise direction, given as:
$$\begin{array}{rcl}
u_{tt}+ku_t+\Delta^2 u+[P-S\int_{\Omega}u_x^2]u_{xx}=g+\alpha u_y & \text{in} & \Omega\times(0,T)\
u=u_{xx}=0 & \text{on} & \Gamma_D\
u_{yy}+\sigma u_{xx}=0,\quad...
In this paper, we investigate the stabilization of a weak viscoelastic wave equation with variable coefficients and an interior delay, which is also subject to a nonlinear boundary dissipation. The existence of weak solution is demonstrated by means of nonlinear semigroup theory. It is noteworthy that the system is non-dissipative. The exponential decay for energy, contingent upon the...
In ultrasound imaging, microbubbles are increasingly being used to improve image resolution. Ultrasound propagation through a bubbly liquid can be modeled using a nonlinear acoustic wave equation for the acoustic pressure coupled to a singular second-order ordinary differential equation for bubble dynamics. Additionally, the wave equation may involve time-fractional dissipation to capture the...
In the presentation we consider constrained optimization problems with equality constraints given by operator $F$ acting between Banach spaces and a number of inequality constraints. The regularity conditions for the this kind of problems ensuring the existence of Lagrange multipliers are expressed with the help e.g. of Robinson Kurcyusz and Zowe or other conditions like Aubin and Guignard,...
In this talk, we consider a freeform optimization problem of eigenvalues in a particle accelerator cavity by means of shape-variations with respect to small deformations. As constraint we utilize the mixed variational formulation by Kikuchi of the normalized Maxwell’s time-harmonic eigenvalue problem. For the eigenvalue optimization, we apply the method of mappings. We show results of...
As rate-independent operators are not smooth, they do not possess classical derivatives. We present results on their generalized derivatives and link them to optimal control problems
This talk deals with infinite horizon optimal control problems governed by time-varying linear parabolic equations. We focus on controls represented by linear combinations of finitely many Dirac measures in the spatial domain, where only one measure is active at any time. This feature endows the problem with switching properties and thus transforms it into an infinite horizon nonsmooth...
We study directional differentiability properties of solution operators of rate-independent evolution variational inequalities with full-dimensional convex polyhedral admissible sets. It is shown that, if the space of continuous functions of bounded variation is used as the domain of definition, then the most prototypical examples of such solution operators - the vector play and stop - are...
This talk explores the application of multi-objective optimization in the field of renewable energy, focusing on both classification and regression tasks driven by machine learning. We consider multiple objectives, including accuracy, computational efficiency, algorithmic bias, and model sparsity. Models can be comprehensive, ranging from complex decision trees and neural networks to simple...
We present a family of discrete optimal control problems that are motivated by quantum pulse optimization to design quantum gates. We solve the continuous relaxation using the gradient ascent pulse engineering (GRAPE) algorithm, and apply combinatorial integral approximation (CIA) techniques to obtain discrete optimal controls. To add constraints and more complex regularization terms, we...
This talk presents a mixed variational formulation for the problem of the elasticity equation with jump conditions in an interface with the purpose of modeling subduction earthquakes by introducing the concept of coseismic jump. For this new problem, we introduced an optimal control problem that seeks to recover the coseismic jump from boundary observations. Both problems can be discretized by...
The present work aims at the application of finite element discretizations to a class of equilibrium problems involving moving constraints. Therefore, a Moreau–Yosida based regularization technique, controlled by a parameter, is discussed. Using an extended $\Gamma$-convergence, a priori convergence is derived. This technique is applied to the discretization of the regularized problems. The...
