This paper studies controlled systems governed by Ito’s stochastic differential equations in which control variables are allowed to enter both drift and diffusion terms. A new verification theorem is derived within the framework of viscosity solutions without involving any derivatives of the value functions. This theorem is shown to have wider applicability than the restrictive classical verifi...

Three-dimensional flow of a low-density polyethylene in a spiral die for blown-film extrusion is simulated. Effect of elongational viscosity on the flow in the spiral die is analyzed. Elongational viscosity is found to have significant effect on the velocity distribution at the die exit and on the pressure and temperature distributions in the die.

In this paper, the nonlinear dynamic buckling of double-walled boron-nitride nanotube (DWBNNT) conveying viscous fluid is investigated based on Eringen's theory. BNNT is modeled as an Euler-Bernoulli beam and is subjected to combine mechanical, electrical and thermal loading. The effect of viscosity on fluid-BNNT interaction is considered based on Navier-Stokes relation. The van der Waals (vdW)...

Nowadays, atomic-force microscopy plays a significant role in nanoscience and nanotechnology, and is widely used for direct measurement at atomic scale and scanning the sample surfaces. In tapping mode, the microcantilever of atomic-force microscope is excited at resonance frequency. Therefore, it is important to study its resonance. Moreover, atomic-force microscopes can be operated in fluid e...

This paper analyzes a class of impulse control problems for multidimensional jump diffusions in the finite time horizon. Following the basic mathematical setup from Stroock and Varadhan [Multidimensional Diffusion Processes, Springer-Verlag, Heidelberg, 2006], this paper first establishes rigorously an appropriate form of the dynamic programming principle. It then shows that the value function ...

We consider homogenization problems in the framework of deterministic optimal control when the dynamics and running costs are completely different in two (or more) complementary domains of the space R . For such optimal control problems, the three first authors have shown that several value functions can be defined, depending, in particular, of the choice is to use only “regular strategies” or ...

A deterministic infinite-horizon singular control problem with unbounded control set is solved completely. The methods used here are those of dynamic programming and viscosity solutions. The novelty is that the value function is convex, C along a piece of the free boundary and not C along another piece of it.

This paper considers an extension of the Merton optimal investment problem to the case where the risky asset is subject to transaction costs and capital gains taxes. We derive the dynamic programming equation in the sense of constrained viscosity solutions. We next introduce a family of functions (Vε)ε>0, which converges to our value function uniformly on compact subsets, and which is character...

Motivated by the work of Fleming [5], we shall provide the general framework to associate inf-sup type values with the Isaacs equations. We shall show that upper and lower bounds for the generators of inf-sup type are upper and lower Hamiltonian in differential games respectively. In particular, lower (resp.upper) bound corresponds to progressive (resp. strictly progressive) strategy. Under Dyn...