相关论文: Optimization of a Nonlinear Acoustics -- Structure…

Motivated by various applications, this article develops the notion of boundary control for Maxwell's equations in the frequency domain. Surface curl is shown to be the appropriate regularization in order for the optimal control problem to…

In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…

In this paper we study a distributed optimal control problem for a nonlocal convective Cahn--Hilliard equation with degenerate mobility and singular potential in three dimensions of space. While the cost functional is of standard tracking…

We propose a time domain decomposition approach to optimal control of partial differential equations (PDEs) based on semigroup theoretic methods. We formulate the optimality system consisting of two coupled forward-backward PDEs, the state…

We consider the control problem of the stochastic Navier-Stokes equations in multidimensional domains introduced in \cite{ocpc} restricted to noise terms defined by Q-Wiener processes. Using a stochastic maximum principle, we derive a…

Autoresonant (continuously phase-locked) two-phase waves of the Korteweg-de-Vries equation are excited and controlled using a two-component, small amplitude, chirped frequency driving. These solutions are analyzed in the weakly nonlinear…

We consider the PDE-constrained optimal control of a leader-follower kinetic opinion formation model, with a Fokker-Planck-type system of partial differential equations as a state constraint. We derive the Boltzmann-type and…

In this paper, a quadratic optimal control problem is considered for second-order parabolic PDEs with homogeneous Dirichlet boundary conditions, in which the "point" control function (depending only on time) constitutes a source term. These…

In this paper we investigate the optimal control problem for a class of stochastic Cauchy evolution problem with non standard boundary dynamic and control. The model is composed by an infinite dimensional dynamical system coupled with a…

Physics-informed neural networks (PINNs) have recently become a popular method for solving forward and inverse problems governed by partial differential equations (PDEs). By incorporating the residual of the PDE into the loss function of a…

We study a topological physics in a one-dimensional nonlinear system by taking an instance of a mechanical rotator model with alternating spring constants. This nonlinear model is smoothly connected to an acoustic model described by the…

We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…

We investigate a quasilinear system consisting of the Westervelt equation from nonlinear acoustics and Pennes bioheat equation, subject to Dirichlet or Neumann boundary conditions. The concept of maximal regularity of type $L_p$-$L_q$ is…

Nonlinear ultrasound imaging leverages harmonic wave generation to enhance contrast and spatial resolution beyond the capabilities of conventional linear techniques. This behavior is commonly modeled by the Westervelt equation, which…

Hydrodynamic modes in the turbulent mixing layer over a cavity can constructively interact with the acoustic modes of that cavity and lead to aeroacoustic instabilities. The resulting limit cycles can cause undesired structural vibrations…

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…

We investigate a distributed optimal control problem for a nonlocal phase field model of viscous Cahn-Hilliard type. The model constitutes a nonlocal version of a model for two-species phase segregation on an atomic lattice under the…

A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…

Linear and nonlinear resonant states can be restrictive: they exist at particular discrete states in frequency and/or elasticity, under particular (e.g., simple-harmonic) waveforms. In forced oscillators, this restrictiveness is an obstacle…

Consider the scattering of a time-harmonic acoustic plane wave by a bounded elastic obstacle which is immersed in a homogeneous acoustic medium. This paper concerns an inverse acoustic-elastic interaction problem, which is to determine the…