in this paper mathematical extensions and generalizations of the pearl-reed model for'growth with saturation are discussed. the derived differential equation are of bernoulli and riccati type that owing to their special forms could be explicitely integrated resulting in closed form solutions. the asymptotic bahaviour of the system in each case is briefly examined and the results are compar...

It is shown that the magnetohydrodynamic equilibrium states of an axisymmetric toroidal plasma with finite resistivity and flows parallel to the magnetic field are governed by a second-order partial differential equation for the poloidal magnetic flux function ψ coupled with a Bernoulli type equation for the plasma density (which are identical in form to the corresponding ideal MHD equilibrium ...

This paper offers new, necessary and sufficient conditions for delay-dependent asymptotic stability of systems of the form 0 1 ( 1) ( ) ( ) x k A x k A x k h + = + − . The time-dependent criteria are derived by Lyapunov’s direct method. Two matrix equations have been derived: matrix polynomial equation and discrete Lyapunov matrix equation. Also, modifications of the existing sufficient conditi...

We consider an optimal control problem with indeenite cost for an abstract model which covers in particular hyperbolic and hyperbolic-like systems in a general bounded domain. Necessary and suucient conditions are given for the synthesis of the optimal control, which is given in terms of the Riccati operator arising from a nonstandard Riccati equation. The theory also extends a nite-dimensional...

We display the performance of the technique called Method of Variational Imbedding for solving the inverse problem of coefficient identification in Euler-Bernoulli equation from over-posed data. The original inverse problem is replaced by a minimization problem. The EulerLagrange equations comprise an eight-order equation for the solution of the original equation and an explicit system of equat...

This paper studies the regularity of an Euler–Bernoulli plate equation on a bounded domain of Rn, n ≥ 2, with partial Neumann control and collocated observation. It is shown that the system is not only well posed in the sense of D. Salamon but also regular in the sense of G. Weiss. It is also shown that the corresponding feedthrough operator is zero.

may be thought of as a nonlinear beam equation. In this paper we obtain both L-L estimates and space-time integrability estimates on solutions to the linear equation. We also use these estimates to study the local existence and asymptotic behavior of solutions to the nonlinear equation, for nonlinear terms which grow like a certain power of u. The main L-L estimate (Theorem 2.1) states that sol...

Let K be a quadratic field, and let ζK its Dedekind zeta function. In this paper we introduce a factorization of ζK into two functions, L1 and L2, defined as partial Euler products of ζK , which lead to a factorization of Riemann’s ζ function into two functions, p1 and p2. We prove that these functions satisfy a functional equation which has a unique solution, and we give series of very fast co...

We present a general series representation formula for the local solution of Bernoulli equation with Caputo fractional derivatives. then focus on generalization logistic and some related numerical simulations.

We consider a system described by the Euler–Bernoulli beam equation. For stabilization, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the controller is a marginally stable positive real function which may contain poles on the imaginary axis. We then give various asymptotical and exponential stability results. We also consider the distur...