To analyze the optimal control of Typhoid fever virus a mathematical modeling was developed by Getachew Teshome Tilahun. We have approached Homotopy Perturbation Method to solve linear differential equation. An analytical solution Susceptible People(S), Infected People (I), Carrier (C), Recovered (R), and Bacteria ( is obtained compared with simulation results. A significant agreement produced ...

In this paper, we formulate a mean-variance portfolio selection model with liability under the constraint that short-selling is prohibited. Due to the introduction of the liability and no-shorting constraints, our problem is not a conventional stochastic optimal linear-quadratic(LQ) control problem, and the corresponding HJB equation has no continuous solution. we construct a lower-semicontinuo...

We prove the uniqueness of the viscosity solution to the Hamilton-Jacobi equation associated with a Bolza problem of the Calculus of Variations, assuming that the Lagrangian is autonomous, continuous, superlinear, and satisfies the usual convexity hypothesis. Under the same assumptions we prove also the uniqueness, in a class of lower semicontinuous functions, of a slightly different notion of ...

In this paper, we prove a comparison result between semicontinuous viscosity sub and supersolutions growing at most quadratically of second-order degenerate parabolic Hamilton-Jacobi-Bellman and Isaacs equations. As an application, we characterize the value function of a finite horizon stochastic control problem with unbounded controls as the unique viscosity solution of the corresponding dynam...

We prove optimality principles for semicontinuous bounded viscosity solutions of HamiltonJacobi-Bellman equations. In particular we provide a representation formula for viscosity supersolutions as value functions of suitable obstacle control problems. This result is applied to extend the Lyapunov direct method for stability to controlled Ito stochastic differential equations. We define the appr...

Balanced Viscosity solutions to rate-independent systems arise as limits of regularized rate-independent flows by adding a superlinear vanishing-viscosity dissipation. We address the main issue of proving the existence of such limits for infinite-dimensional systems and of characterizing them by a couple of variational properties that combine a local stability condition and a balanced energy-di...

Adequate clay minerals considerably affect the macroscopic mechanical behavior of water even at concentrations of a few percent. Thus when 2 wt. % laponite clay mineral nanoparticles are added to water, the resulting colloidal suspension after some time takes on the semisolid characteristics of a jellylike material at room temperature. Cold neutron time-of-flight spectroscopy data are in agreem...

We revisit the pioneering work of Bressan & Hong on deterministic control problems in stratified domains, i.e. control problems for which the dynamic and the cost may have discontinuities on submanifolds of R . By using slightly different methods, involving more partial differential equations arguments, we (i) slightly improve the assumptions on the dynamic and the cost; (ii) obtain a compariso...