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In this paper, we obtain the existence of time optimal control of the Korteweg-de Vries-Burgers equation in a bounded domain with control acting locally in a subset. Moreover, we prove that any time optimal control satisfies the bang–bang property.
We are interested in shape sensitivity analysis for an optimization problem arising in medical applications of high intensity focused ultrasound. The goal is to find the optimal shape of a focusing acoustic lens so that the desired acoustic pressure at a kidney stone is achieved. Coupling of the...
This study addresses well-posedness of a Mindlin–Timoshenko (MT) plate model that incorporates nonlinear viscous damping and nonlinear source term in Neumann boundary conditions. The main results verify local and global existence of solutions as well as their continuous dependence on the initial...
We consider an optimal control problem arising in the context of economic theory of growth, on the lines of the works by Skiba and Askenazy–Le Van. The framework of the model is intertemporal infinite horizon utility maximization. The dynamics involves a state variable representing total...
We consider the problem of maximizing the expected amount of time an exponential martingale spends above a constant threshold up to a finite time horizon. We assume that at any time the volatility of the martingale can be chosen to take any value between
In this paper, we consider an option pricing problem in a pure jump model where the process X(t) models the logarithm of the stock price. By the Schauder fixed point theorem, we show the existence and uniqueness of the solutions in H
lder spaces for the European and...
We consider the wave equation with Dirichlet–Neumann boundary conditions on a family of perturbed domains
. We discuss the shape differentiability analysis associated with the above mentioned problem, namely the existence of strong material and shape derivatives of the...
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