Related papers: On the transport limit of singularly perturbed con…
This paper considers two types of boundary control problems for linear transport equations. The first one shows that transport solutions on a subdomain of a domain X can be controlled exactly from incoming boundary conditions for X under…
We generalize leading-order asymptotics of a form of the heat content of a submanifold (van den Berg & Gilkey 2015) to the setting of time-dependent diffusion processes in the limit of vanishing diffusivity. Such diffusion processes arise…
Motion in the atmosphere or mantle convection are two among phenomena of natural convection induced by internal heat sources. They bifurcate from the conduction state as a result of its loss of stability. In spite of their importance, due…
We study the large scale evolution of a scalar lattice excitation which satisfies a discrete wave-equation in three dimensions. We assume that the dispersion relation associated to the elastic coupling constants of the wave-equation is…
The linear singularly perturbed convection-diffusion problem in one dimension is considered and its discretization on a Bakhvalov-type mesh is analyzed. The preconditioning technique is used to obtain the pointwise convergence uniform in…
Light diffusion is usually associated with thick, opaque media. Indeed, multiple scattering is necessary for the onset of the diffusive regime and such condition is generally not met in almost transparent media. Nonetheless, at long enough…
In this paper we analyse a boundary value problem for the Laplace equation with a nonlinear non-autonomous transmission conditions on the boundary of a small inclusion of size $\epsilon$. We show that the problem has solutions for…
We study diffusions, variational principles and associated boundary value problems on directed graphs with natural weightings. Using random walks and exit times, we associate to certain subgraphs (domains) a pair of sequences, each of which…
In this study, we analyze the behavior of monotone traveling waves of a one-dimensional porous medium equation modeling mechanical properties of living tissues. We are interested in the asymptotics where the pressure, which governs the…
We consider the diffusive limit of a steady neutron transport equation with one-speed velocity in a two-dimensional annulus. A classical theorem states that the solution can be approximated in $L^{\infty}$ by the leading order interior…
Starting from full-dimensional models of solute transport, we derive and analyze multi-dimensional models of time-dependent convection, diffusion, and exchange in and around pulsating vascular and perivascular networks. These models are…
Soliton transport in tube-like networks is studied by solving the nonlinear Schroedinger equation (NLSE) on finite thickness ("fat") graphs. The dependence of the solution and of the reflection at vertices on the graph thickness and on the…
The paper investigates the throughput behavior of single-commodity dynamical flow networks governed by monotone distributed routing policies. The networks are modeled as systems of ODEs based on mass conversation laws on directed graphs…
A simple finite element formulation of the outlet gradient boundary condition is presented in the general context of convective-diffusive transport processes. Basically, the method is based on an upstream evaluation of the dependent…
Diffusive transport of particles or, more generally, small objects is a ubiquitous feature of physical and chemical reaction systems. In configurations containing confining walls or constrictions transport is controlled both by the…
We consider a transport-diffusion equation forced by random noise of three types: additive, linear multiplicative in It$\hat{\mathrm{o}}$'s interpretation, and transport in Stratonovich's interpretation. Via convex integration modified to…
Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are…
We consider the problem of optimizing heat transport through an incompressible fluid layer. Modeling passive scalar transport by advection-diffusion, we maximize the mean rate of total transport by a divergence-free velocity field. Subject…
In this work we consider an interface logistic problem where two populations live in two different regions, separated by a membrane or interface where it happens an interchange of flux. Thus, the two populations only interact or are coupled…
This paper considers distributed resource allocation and sum-preserving constrained optimization over lossy networks, where the links are unreliable and subject to packet drops. We define the conditions to ensure convergence under packet…