Related papers: Energy Estimates for Low Regularity Bilinear Schr\…
The covariant Klein-Gordon equation requires twice the boundary conditions of the Schrodinger equation and does not have an accepted single-particle interpretation. Instead of interpreting its solution as a probability wave determined by an…
We provide pointwise upper bounds for the transition kernels of semigroups associated with a class of systems of nondegenerate elliptic partial differential equations with unbounded coefficients with possibly unbounded diffusion…
We prove a Carleman estimate for a one-dimensional parabolic equation which degenerates at one extremity of the domain and has a bounded, time dependent coefficient multiplying the diffusion term. Then we use the estimate to show the null…
In this letter, we derive minimum-energy controls for a broad class of control-affine systems using a Lagrange multiplier fixed-point equation and a generally non-symmetric Gramian-like matrix. In feasible coercivity classes, this fixed…
In this paper, we study the null controllability of weakly degenerate coupled parabolic systems with two different diffusion coefficients and one control force. To obtain this aim, we develop first new global Carleman estimates for…
In this article, stability estimates are given for the determination of the zeroth-order bounded perturbations of the biharmonic operator when the boundary Neumann measurements are made on the whole boundary and on slightly more than half…
Using recently developed techniques based on scattering theory, we find the electromagnetic Casimir energy for geometries involving semi-infinite planes, a case that is of particular interest in the design of microelectromechanical devices.…
We consider the Schr\"odinger partial differential equation of a rotating symmetric rigid molecule (symmetric rotor) driven by a z-linearly polarized electric field, as prototype of degenerate infinite-dimensional bilinear control system.…
In this paper, we prove several new results that give new insights into bilinear systems. We discuss conditions for asymptotic stability using probabilistic arguments. Moreover, we provide a global characterization of reachability in…
We present an analytic example of two dimensional quantum mechanical system, where the exponential suppression of the probability of over-barrier reflection changes non-monotonically with energy. The suppression is minimal at certain…
We consider the initial value problem for the inhomogeneous nonlinear Schr\"odinger equation with double nonlinearities (DINLS) \begin{equation*} i \partial_t u + \Delta u = \lambda_1 |x|^{-b_1}|u|^{p_1}u +…
In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…
For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial differential control systems and control systems…
Three-body systems in two dimensions with zero-range interactions are considered for general masses and interaction strengths. The problem is formulated in momentum space and the numerical solution of the Schr\"odinger equation is used to…
We consider Fokker--Planck--Kolmogorov equations with unbounded coefficients and obtain upper estimates of solutions. We also obtain new estimates involving Lyapunov functions.
We consider Schr{\"o}dinger equations with logarithmic nonlinearity and bilinear controls, posed on $\mathbb{T}^d$ or $\mathbb{R}^d$. We prove their small-time global $L^2$-approximate controllability. The proof consists in extending to…
Controllability and observability energy functions play a fundamental role in model order reduction and are inherently connected to optimal control problems. For linear dynamical systems the energy functions are known to be quadratic…
An alternative approximation scheme has been used in solving the Schrodinger equation for the exponential-cosine-screened Coulomb potential. The bound state energ\i es for various eigenstates and the corresponding wave functions are…
The explicit analytical expression for the distribution function of parametric derivatives of energy levels ("level velocities") with respect to a random change of scattering potential is derived for the chaotic quantum systems belonging to…
In this paper, we examine the question of the boundary controllability of the one-dimensional non-isentropic Euler equation for compressible polytropic gas, in the context of weak entropy solutions. We consider the system in Eulerian…