相关论文: Control estimates for 0th order pseudodifferential…

This article is devoted to studying the null controllability of evolution equations with memory terms. The problem is challenging not only because the state equation contains memory terms but also because the classical controllability…

We adopt the integral definition of the fractional Laplace operator and analyze an optimal control problem for a fractional semilinear elliptic partial differential equation (PDE); control constraints are also considered. We establish the…

We consider a bilinear optimal control for an evolution equation involving the fractional Laplace operator of order $0<s<1$. We first give some existence and uniqueness results for the considered evolution equation. Next, we establish some…

In this paper, we derive explicit second-order necessary and sufficient optimality conditions of a local minimizer to an optimal control problem for a quasilinear second-order partial differential equation with a piecewise smooth but not…

We study several aspects of the dynamic programming approach to optimal control of abstract evolution equations, including a class of semilinear partial differential equations. We introduce and prove a verification theorem which provides a…

Let $\Delta$ be the Dirichlet Laplacian on the interval $(0,\pi)$. The null controllability properties of the equation $$u_{tt}+\Delta^2 u+\rho (\Delta)^\alpha u_t=F(x,t)$$ are studied. Let $T>0$, and assume initial conditions $(u^0,u^1)\in…

We study a class of stochastic control problems where a cost of the form \begin{equation}\mathbb{E}\int_{[0,\infty)}e^{-\beta s}[\ell(X_s) ds+h(Y^{\circ}_s) d|Y|_s]\end{equation} is to be minimized over control processes $Y$ whose…

This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…

In this paper we make a subtle use of operator theory techniques and the well-known Schauder fixed-point principle to establish the existence of pseudo-almost automorphic solutions to some second-order damped integro-differential equations…

Recent results have revealed a critical way in which lower order terms affect the well-posedness of the characteristic initial value problem for the scalar wave equation. The proper choice of such terms can make the Cauchy problem for…

We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered…

We derive conditions for the propagation of monotone ordering properties for a class of nonlinear parabolic partial differential equation (PDE) systems on metric graphs. For such systems, PDE equations with a general nonlinear dissipation…

Using the exact path integral solution for the damped harmonic oscillator it is shown that in general there does not exist an exact dissipative Liouville operator describing the dynamics of the oscillator for arbitrary initial bath…

This paper is concerned with the null controllability problem for a class of quasilinear parabolic equations under multiplicative control, locally supported in space. For the purpose of proving the existence of a multiplicative control…

We consider an abstract evolution equation with linear damping, a nonlinear term of Duffing type, and a small forcing term. The abstract problem is inspired by some models for damped oscillations of a beam subject to external loads or…

We study an asymptotic preserving scheme for the temporal discretization of a system of parabolic semilinear SPDEs with two time scales. Owing to the averaging principle, when the time scale separation $\epsilon$ vanishes, the slow…

We study the exact controllability of the evolution equation \begin{equation*} u'(t)+Au(t)+p(t)Bu(t)=0 \end{equation*} where $A$ is a nonnegative self-adjoint operator on a Hilbert space $X$ and $B$ is an unbounded linear operator on $X$,…

Many physical phenomena, governed by partial differential equations (PDEs), are second order in nature. This makes sense to pose the control on the second order derivatives of the field solution, in addition to zero and first order ones, to…

We present a fully discrete finite element method for the interior null controllability problem subject to the wave equation. For the numerical scheme, piece-wise affine continuous elements in space and finite differences in time are…

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…