ISSN:

1556-1801

eISSN:

1556-181X

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## Networks and Heterogeneous Media

February 2022 , Volume 17 , Issue 1

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**Abstract:**

In [Andreianov, Coclite, Donadello, Discrete Contin. Dyn. Syst. A, 2017], a finite volume scheme was introduced for computing vanishing viscosity solutions on a single-junction network, and convergence to the vanishing viscosity solution was proven. This problem models

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**Abstract:**

We investigate the homogenization through

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**Abstract:**

We study the asymptotic behavior of a three-dimensional elastic material reinforced with highly contrasted thin vertical strips constructed on horizontal iterated Sierpinski gasket curves. We use

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**Abstract:**

Hyperbolic systems on networks often can be written as systems of first order equations on an interval, coupled by transmission conditions at the endpoints, also called port-Hamiltonians. However, general results for the latter have been difficult to interpret in the network language. The aim of this paper is to derive conditions under which a port-Hamiltonian with general linear Kirchhoff's boundary conditions can be written as a system of

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**Abstract:**

We consider nonlinear scalar conservation laws posed on a network. We define an entropy condition for scalar conservation laws on networks and establish $L^1$ stability, and thus uniqueness, for weak solutions satisfying the entropy condition. We apply standard finite volume methods and show stability and convergence to the unique entropy solution, thus establishing existence of a solution in the process. Both our existence and stability/uniqueness theory is centred around families of stationary states for the equation. In one important case – for monotone fluxes with an upwind difference scheme – we show that the set of (discrete) stationary solutions is indeed sufficiently large to suit our general theory. We demonstrate the method's properties through several numerical experiments.

2020
Impact Factor: 1.213

5 Year Impact Factor: 1.384

2020 CiteScore: 1.9

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