Related papers: New Coupling Conditions for Isentropic Flow on Net…
Robustness of routing policies for networks is a central problem which is gaining increased attention with a growing awareness to safeguard critical infrastructure networks against natural and man-induced disruptions. Routing under limited…
We present explicit sufficient conditions that guarantee the existence and uniqueness of the feasible load-flow solution for distribution networks with a generic topology (radial or meshed) modeled with positive sequence equivalents. In the…
We continue our analysis of the coupling between nonlinear hyperbolic problems across possibly resonant interfaces. In the first two parts of this series, we introduced a new framework for coupling problems which is based on the so-called…
We study enhancement of diffusive mixing on a compact Riemannian manifold by a fast incompressible flow. Our main result is a sharp description of the class of flows that make the deviation of the solution from its average arbitrarily small…
We investigate the vacuum in nonisentropic gas dynamics in one space variable, with the most general equation of states allowed by thermodynamics. We recall physical constraints on the equations of state and give explicit and easily…
We study the global well-posedness and asymptotic behavior for a semilinear damped wave equation with Neumann boundary conditions, modelling a one-dimensional linearly elastic body interacting with a rigid substrate through an adhesive…
The aggregation equation arises naturally in kinetic theory in the study of granular media, and its interpretation as a 2-Wasserstein gradient flow for the nonlocal interaction energy is well-known. Starting from the spatially homogeneous…
In this paper, a mathematical framework for the coupling of gas networks to electric grids is presented to describe in particular the transition from gas to power. The dynamics of the gas flow are given by the isentropic Euler equations,…
This paper addresses the well posedness of a dynamical model of perfect plasticity with mixed boundary conditions for general closed and convex elasticity sets. The proof relies on an asymptotic analysis of the solution of a perfect…
When modeling vehicular traffic flow on highway networks via macroscopic models, suitable coupling conditions at the network nodes are crucial. Frequently, the evolution of traffic flow on each network edge is described in a lane-averaged…
Relative permeability is commonly used to model immiscible fluid flow through porous materials. In this work we derive the relative permeability relationship from conservation of energy, assuming that the system to be non-ergodic at large…
In the physically non viscous fluid dynamics, "shock capturing" methods adopt either an artificial viscosity contribution or an appropriate Riemann solver algorithm. These techniques are necessary to solve the strictly hyperbolic Euler…
We propose new Kruzhkov type entropy conditions for one dimensional scalar conservation law with a discontinuous flux. We prove existence and uniqueness of the entropy admissible weak solution to the corresponding Cauchy problem merely…
An important problem in the theory of compressible gas flows is to understand the singular behavior of vacuum states. The main difficulty lies in the fact that the system becomes degenerate at the vacuum boundary, where the characteristics…
This work focuses on the Riemann problem of Euler equations with global constant initial conditions and a single-point heating source, which comes from the physical problem of heating one-dimensional inviscid compressible constant flow. In…
We are concerned with the global existence of entropy solutions for the compressible Euler equations describing the gas flow in a nozzle with general cross-sectional area, for both isentropic and isothermal fluids. New viscosities are…
We introduce in this contribution the notion of partial Riemann problem. Recall that the Riemann problem describes a shock tube interaction between two given states ; the partial Riemann problem is a generalization of the previous concept…
We study deterministic continuous-time lossy dynamical flow networks with constant exogenous demands, fixed routing, and finite flow and buffer capacities. In the considered model, when the total net flow in a cell ---consisting of the…
A noteworthy aspect in blood flow modeling is the definition of the mechanical interaction between the fluid flow and the biological structure that contains it, namely the vessel wall. It has been demonstrated that the addition of a viscous…
We establish the global existence of weak entropy solutions for 1D isentropic gas dynamics with general pressure laws ($\gamma > 1$). To address vacuum degeneracy, we introduce a novel structural regularization via a "Synchronized Dual…