Operational WKB solution to the initial/final-value problem for Beechem-Haas equations.
Operator type expansion-compression fixed point theorem.
Opial inequalities on time scales
We present a version of Opial's inequality for time scales and point out some of its applications to so-called dynamic equations. Such dynamic equations contain both differential equations and difference equations as special cases. Various extensions of our inequality are offered as well.
Opial's type inequalities on time scales and some applications
We prove some new Opial type inequalities on time scales and employ them to prove several results related to the spacing between consecutive zeros of a solution or between a zero of a solution and a zero of its derivative for second order dynamic equations on time scales. We also apply these inequalities to obtain a lower bound for the smallest eigenvalue of a Sturm-Liouville eigenvalue problem on time scales. The results contain as special cases some results obtained for second order differential...
Opposing flows in a one dimensional convection-diffusion problem
In this paper, we examine a particular class of singularly perturbed convection-diffusion problems with a discontinuous coefficient of the convective term. The presence of a discontinuous convective coefficient generates a solution which mimics flow moving in opposing directions either side of some flow source. A particular transmission condition is imposed to ensure that the differential operator is stable. A piecewise-uniform Shishkin mesh is combined with a monotone finite difference operator...
Optimal, adaptive and single state feedback control for a 3D chaotic system with golden proportion equilibria
In this paper, the problems on purposefully controlling chaos for a three-dimensional quadratic continuous autonomous chaotic system, namely the chaotic Pehlivan-Uyaroglu system are investigated. The chaotic system, has three equilibrium points and more interestingly the equilibrium points have golden proportion values, which can generate single folded attractor. We developed an optimal control design, in order to stabilize the unstable equilibrium points of this system. Furthermore, we propose...
Optimal conditions for maximum and antimaximum principles of the periodic solution problem.
Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations
Nonimprovable, in a sense sufficient conditions guaranteeing the unique solvability of the problem where is a linear bounded operator, , and , are established.
Optimal Control of a Cancer Cell Model with Delay
In this paper, we look at a model depicting the relationship of cancer cells in different development stages with immune cells and a cell cycle specific chemotherapy drug. The model includes a constant delay in the mitotic phase. By applying optimal control theory, we seek to minimize the cost associated with the chemotherapy drug and to minimize the number of tumor cells. Global existence of a solution has been shown for this model and existence...
Optimal control of combined therapy in a single strain HIV-1 model.
Optimal control of impulsive stochastic evolution inclusions
In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions driven by vector measures. We use stochastic vector measures as controls adapted to an increasing family of complete sigma algebras and prove the existence of optimal controls.
Optimal control of nonlinear evolution equations
In this paper, first we consider parametric control systems driven by nonlinear evolution equations defined on an evolution triple of spaces. The parametres are time-varying probability measures (Young measures) defined on a compact metric space. The appropriate optimization problem is a minimax control problem, in which the system analyst minimizes the maximum cost (risk). Under general hypotheses on the data we establish the existence of optimal controls. Then we pass to nonparametric...
Optimal control of nonlinear second order evolution equations.
Optimal control of semilinear evolution inclusions via discrete approximations
Optimal control of stabilizable time-varying linear systems with time delay
Optimal control under discrete observation of continuous stochastic systems with time delay
Optimal controllability of impulsive control systems.
Optimal Convective Heat-Transport
The one-dimensional steady-state convection-diffusion problem for the unknown temperature of a medium entering the interval with the temperature and flowing with a positive velocity is studied. The medium is being heated with an intensity corresponding to for a constant . We are looking for a velocity with a given average such that the outflow temperature is maximal and discuss the influence of the boundary condition at the point on the “maximizing” function .
Optimal design of turbines with an attached mass
We minimize, with respect to shape, the moment of inertia of a turbine having the given lowest eigenfrequency of the torsional oscillations. The necessary conditions of optimality in conjunction with certain physical parameters admit a unique optimal design.
Optimal design of turbines with an attached mass
We minimize, with respect to shape, the moment of inertia of a turbine having the given lowest eigenfrequency of the torsional oscillations. The necessary conditions of optimality in conjunction with certain physical parameters admit a unique optimal design.