Related papers: On the transport limit of singularly perturbed con…

This paper studies the problem of output agreement in networks of nonlinear dynamical systems under time-varying disturbances, using dynamic diffusive couplings. Necessary conditions are derived for general networks of nonlinear systems,…

We derive conditions for the propagation of monotone ordering properties for a class of nonlinear parabolic partial differential equation (PDE) systems on metric graphs. For such systems, PDE equations with a general nonlinear dissipation…

We propose a new approach to graph compression by appeal to optimal transport. The transport problem is seeded with prior information about node importance, attributes, and edges in the graph. The transport formulation can be setup for…

We deal with the rigorous homogenization and dimension reduction of flow and transport problems posed in thin $\varepsilon$-periodic perforated layers with thickness of order $\varepsilon^{\alpha}$ with $\alpha \in (0,1)$ and therefore the…

In this article, a parameter-uniform numerical method is presented to solve one-dimensional singularly perturbed parabolic convection-diffusion turning point problem exhibiting two exponential boundary layers. We study the asymptotic…

We are interested in evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a…

Consider a network embedded in the 2D plane, where a particle diffuses along the edges of the network. It is clear that over short length scales a particle moves along a single edge and thus undergoes one-dimensional diffusion. However, on…

We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…

In this article, we have considered a time-dependent two-parameter singularly perturbed parabolic problem with discontinuous convection coefficient and source term. The problem contains the parameters $\epsilon$ and $\mu$ multiplying the…

We consider the transport equation on $[0,T]\times \mathbb{R}^n$ in the situation where the vector field is $BV$ off a set $S\subset [0,T]\times \mathbb{R}^n$. We demonstrate that solutions exist and are unique provided that the set of…

A two-parameter singularly perturbed problem with discontinuous source and convection coefficient is considered in one dimension. Both convection coefficient and source term are discontinuous at a point in the domain. The presence of…

We introduce the notion of a network's conduciveness, a probabilistically interpretable measure of how the network's structure allows it to be conducive to roaming agents, in certain conditions, from one portion of the network to another.…

This paper concerns wave propagation in a class of scalar reaction-diffusion-convection equations with $p$-Laplacian-type diffusion and monostable reaction. We introduce a new concept of a non-smooth traveling wave profile, which allows us…

We consider a dissipative flow network that obeys the standard linear nodal flow conservation, and where flows on edges are driven by potential difference between adjacent nodes. We show that in the case when the flow is a monotonically…

We consider cross-diffusion systems describing evolution of two species $u$ and $v$ moving according to Darcy's law with the pressure law $p(s) = \frac{1}{\alpha-1} s^{\alpha-1}$ where $s=u+v$. One of the most challenging questions in the…

In this paper, we derive a stability result for $L_1$ and $L_{\infty}$ perturbations of diffusions under weak regularity conditions on the coefficients. In particular, the drift terms we consider can be unbounded with at most linear growth,…

We consider a one dimensional transport equation with varying vector field and a small viscosity coefficient, controlled by one endpoint of the interval. We give upper and lower bounds on the minimal time needed to control to zero,…

This paper is devoted to the diffusive limit of the nonlinear radiative heat transfer system with curved boundary domain (\textit{two dimensional disk}). The solution constructed in \cite{ghattassi2022convergence} by the leading order…

The problem of electron scattering on the one-dimensional complexes is considered. We propose a novel theoretical approach to solution of the transport problem for a quantum graph. In the frame of the developed approach the solution of the…

We consider an optimal transport problem on the unit simplex whose solutions are given by gradients of exponentially concave functions and prove two main results. First, we show that the optimal transport is the large deviation limit of a…