We consider the bilinear optimal control of an advection-reaction-diffusion system, where arises as velocity field in advection term. Such a problem is generally challenging from both theoretical analysis and algorithmic design perspectives, mainly because state variable depends nonlinearly on and, additional divergence-free constraint coupled together with equation. Mathematically, proof exist...

As an alternative to the particle tracking-based residence time calculations, a finite difference approach using the conventional advection-diffusion-reaction kinetics equation for describing the evolution of the residence time field is derived. Advection and mixing of water masses is accompanied with their ageing following a simple zero-order kinetics rule. The governing equations are solved b...

<p style='text-indent:20px;'>In this study, we consider a Lotka–Volterra reaction–diffusion–advection model for two competing species under homogeneous Dirichlet boundary conditions, describing hostile environment at the boundary. In particular, deal with case in which one diffuses constant rate, whereas other has rate diffusion directed movement toward better habitat heterogeneous lethal...

Water exchange mechanisms are assessed via modelling the spatial distribution of the mean residence time in lakes and coastal areas. A grid-based numerical solution of the deterministic advection-diffusion-reaction kinetics equation with the ageing of water as transport variable is applied. The composition of residence time from times spent over separate sub-domains is handled as multi-species ...

Abstract. An operator-splitting algorithm is presented for the solution of a partial differential equation arising in the modeling of deposition processes in sand mechanics. Sand piles evolution is modeled by an advection-diffusion equation, with a non-smooth diffusion operator that contains a point-wise constraint on the gradient of the solution. Piecewise linear finite elements are used for t...

Background: solute transport in highly heterogeneous media and even neutron diffusion nuclear environments are among the numerous applications of fractional differential equations (FDEs), being demonstrated by field experiments that concentration profiles exhibit anomalous non-Fickian growth rates so-called “heavy tails”. Methods: a nonlinear-coupled 3D hydro-mechanical model accounting for (FD...

A discontinuous Galerkin (dG) method for the numerical solution of initial/boundary value multicompartment partial differential equation models, interconnected with interface conditions, is presented and analyzed. The study of interface problems is motivated by models of mass transfer of solutes through semipermeable membranes. More specifically, a model problem consisting of a system of semili...