A constructive method is developed to design inverse optimal controllers for a class of linear distributed parameter systems (DPSs). Inverse optimality guarantees that the cost functional to be minimized is meaningful in the sense that the symmetric and positive definite weighting kernel matrix on the states is chosen after the control design instead of being specified at the start of the contr...

We study the Bernoulli property for a class of partially hyperbolic systems arising from skew products. More precisely, we consider map $(T,M,\mu )$, where $\mu$ is Gibbs measure, an aperiodic Hölder continuous cocycle $\phi :M\to \mathbb {R}$ with zero mean and zero-entropy flow $(K_t,N,\nu )$. then product \begin{equation*} T_\phi (x,y)=(Tx,K_{\phi (x)}y), \end{equation*} acting on $(M\times...

We consider a coupled PDE system arising in noise reduction problems. In a two dimensional chamber, the acoustic pressure (unwanted noise) is represented by a hyperbolic wave equation. The floor of the chamber is subject to the action of piezo-ceramic patches (smart materials). The goal is to reduce the acoustic pressure by means of the vibrations of the floor which is modelled by a hyperbolic ...

We establish existence and uniqueness of generalized solutions to the initial-boundary value problem corresponding to an Euler-Bernoulli beam model from mechanics. The governing partial differential equation is of order four and involves discontinuous, and even distributional, coefficients and right-hand side. The general problem is solved by application of functional analytic techniques to obt...

We are concerned with the existence and stability of multidimensional transonic shocks for the Euler equations for steady potential compressible fluids. The Euler equations, consisting of the conservation law of mass and the Bernoulli law for the velocity, can be written as the following second-order nonlinear equation of mixed elliptic-hyperbolic type for the velocity potential φ : Ω ⊂ R → R: ...

The aim of this paper is to find the numerical solutions of the second order linear and nonlinear differential equations with Dirichlet, Neumann and Robin boundary conditions. We use the Bernoulli polynomials as linear combination to the approximate solutions of 2nd order boundary value problems. Here the Bernoulli polynomials over the interval [0, 1] are chosen as trial functions so that care ...

In the present analysis, an infinite Euler– Bernoulli beam of constant cross-section resting on an elastic foundation is considered. The beam and foundation are assumed to be homogeneous and isotropic. The foundation is modeled using one parameter without damping. The beam is subjected to a constant point load moving with a constant speed along the beam. An effort has been made to find the solu...

This article consists of Improved Bernoulli Sub-Equation Function Method (IBSEFM) to get the new solutions nonlinear fractional Schrödinger equation described by beta-derivative. Foremost, it is dealt with derivative Atangana. Secondly, basic properties IBSEFM are given. Finally, proposed method has been applicated considered its solutions. Moreover, graphs obtained plotted via Mathematica. It ...