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

In this paper a study to application of Least Squares Finite Element Method (LSFEM) is made and with auxiliary equations (temperature derivatives) in the solution of Transient Three-dimensional Diffusion-Reaction. In order to do so, two applications are presented and discussed, one of them Pure Diffusion and another DiffusionReaction, both solved towards the constructive meshes with hexahedron ...

In the paper, we investigate a three-species food chain model with diffusion and ratio-dependent predation functional response. We mainly focus on the co-existence of the three species. For this coupled reaction-diffusion system, we study the persistent property of the solution, the stability of the constant positive steady state solution, and the existence and non-existence of non-constant pos...

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...

Electrostatic interactions strongly affect the immersion depth of nanoparticles into an interface. We prove this statement by measuring the diffusion constant of charged nanoparticles at a sodium chloride solution/air interface. Interfacial diffusion of nanoparticles slows down with increasing ionic strength of the sodium chloride solution. Hydrodynamic calculations are used to estimate the imm...

We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop. When the diffusion 6oefficients are large, this solution represents a stable, spatially homogeneous time-periodic solution of the PDE. We show that when the diffusion coefficients become small, the spatially homoge...

The stochastic solution to a diffusion equations with polynomial coefficients is called a Pearson diffusion. If the first time derivative is replaced by a Caputo fractional derivative of order less than one, the stochastic solution is called a fractional Pearson diffusion. This paper develops an explicit formula for the covariance function of a fractional Pearson diffusion in steady state, in t...

In the paper, we investigate a three-species food chain model with diffusion and ratio-dependent predation functional response. We mainly focus on the coexistence of the three species. For this coupled reaction-diffusion system, we study the persistent property of the solution, the stability of the constant positive steady state solution, and the existence and nonexistence of nonconstant positi...

BACKGROUND Gap junctions (GJs) are intercellular channels through which molecules smaller than 1 kDa can diffuse, and they have been suggested as drug targets. To develop chemical drugs acting on this target, a high-throughput screening (HTS) system for GJ modulators is necessary. RESULTS We designed a new, high-throughput GJ intercellular communication (GJIC) assay. This assay system consist...

-Recent progress in the development of coarse-mesh nodal methods for the numerical solution of the neutron diffusion and transport equations is reviewed. In contrast with earlier nodal simulators, more recent nodal diffusion methods are characterized by the systematic derivation of spatial coupling relationships that are entirely consistent with the multigroup diffusion equation. These relation...