The purpose of this paper is to describe the application of the notion of viscosity solutions to solve the Hamilton–Jacobi–Bellman (HJB) equation associated with an important class of optimal control problems for quantum spin systems. The HJB equation that arises in the control problems of interest is a first-order nonlinear partial differential equation defined on a Lie group. Hence we employ ...

The purpose of present problem is to studies of effects of variable viscosity and heat source on unsteady laminar flow of dusty conducting fluid between parallel porous plates through porous medium with temperature dependent viscosity. The fluid is considered as unsteady laminar flow through porous medium and acted upon by a constant pressure gradient and an external uniform magnetic field is a...

Forced displacement of oil by polymer flooding in oil reservoir is one of the effective methods of enhanced (tertiary) oil recovery. A classical model of this process within Hele-Shaw approximation involves three-layer fluid in a Hele-Shaw cell having a variable viscosity fluid in the intermediate layer between oil and water. The goal here is to find an optimal viscosity profile of the intermed...

We derive the relativistic equations for stellar perturbations, including in a consistent way shear viscosity in the stress-energy tensor, and we numerically integrate our equations in the case of large viscosity. We consider the slow rotation approximation, and we neglect the coupling between polar and axial perturbations. In our approach, the frequency and damping time of the emitted gravitat...

[1] We investigate the physics of multiscale convection in Earth’s mantle, characterized by the coexistence of large-scale mantle circulation associated with plate tectonics and small-scale sublithospheric convection. In this study, conditions for the existence of smallscale convection beneath oceanic lithosphere are investigated by deriving a scaling law for the onset of convection in a fluid ...

Let u(x; t) be the possibly discontinuous entropy solution of a nonlinear scalar conservation law with smooth initial data. Suppose u"(x; t) is the solution of an approximate viscosity regularization, where " > 0 is the small viscosity amplitude. We show that by post-processing the small viscosity approximation u", we can recover pointwise values of u and its derivatives with an error as close ...

A rate-independent model coupling small-strain associative elasto-plasticity and damage is studied via a vanishing-viscosity analysis with respect to all the variables describing system. This extends performed for same system in [V. Crismale G. Lazzaroni, Calc. Var. Partial Differential Equations, 55 (2016), 17], where regularization involving only variable was set forth. In present work, an ad...

In this note we present some of our recent results concerning flows with pressure and shear dependent viscosity. From the numerical point of view several problems arise, first from the difficulty of approximating incompressible velocity fields and, second, from poor conditioning and possible lack of differentiability of the involved nonlinear functions due to the material laws. The lack of diff...

About the "normal growth" approximation in the dynamical theory of phase transitions L. Truskinovsky Nonequilibrium phase transitions can often be modeled by a surface of dis-continuity propagating into a metastable region. The physical hypothesis of "normal growth" presumes a linear relation between the velocity of the phase boundary and the degree of metastability. The phenomenological coeffi...

A new approximation technique based on L1-minimization is introduced. It is proven that the approximate solution converges to the viscosity solution in the case of one-dimensional stationary Hamilton–Jacobi equation with convex Hamiltonian. Mathematics Subject Classification (2000) 65N35 · 65N22 · 65F05 · 35J05