54 citations · 138 across the 17 of their papers we have counts for
18 papers
Local Asymptotic Patterns for Viscous Approximations of Conservation Laws
Alberto Bressan, Laura Caravenna, Wen Shen
Solutions to hyperbolic conservation laws can be approximated in many different ways: by vanishing viscosity, relaxations, discrete or semi-discrete numerical schemes, approximatio…
Chemotaxis models with signal-dependent sensitivity and a logistic-type source, II: Persistence and stabilization
Le Chen, Ian Ruau, Wenxian Shen
This paper is Part II of a series on boundedness, global existence, and asymptotic behavior of positive classical solutions to the chemotaxis model $$\begin{cases} u_t=Δu-χ_0\nabla…
A Uniqueness Condition for Conservation Laws with Discontinuous Gradient-Dependent Flux
Alberto Bressan, Wen Shen
The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions or , when th…
Conservation Laws with Discontinuous Gradient-Dependent Flux: the Stable Case
Debora Amadori, Alberto Bressan, Wen Shen
The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions or , when th…
Conservation Laws with Discontinuous Gradient-Dependent Flux: the Unstable Case
Debora Amadori, Alberto Bressan, Wen Shen
The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions or , when th…
A Space-time Nonlocal Traffic Flow Model: Relaxation Representation and Local Limit
Qiang Du, Kuang Huang, James Scott +1
We propose and study a nonlocal conservation law modelling traffic flow in the existence of inter-vehicle communication. It is assumed that the nonlocal information travels at a fi…
The Cauchy Problem for a non Strictly Hyperbolic System of Conservation Laws Arising in Polymer Flooding
Graziano Guerra, Wen Shen
We study the Cauchy problem of a system of conservation laws modeling two--phase flow of polymer flooding in rough porous media with possibly discontinuous permeability…
Entropy Admissibility of the Limit Solution for a Nonlocal Model of Traffic Flow
Alberto Bressan, Wen Shen
We consider a conservation law model of traffic flow, where the velocity of each car depends on a weighted average of the traffic density ahead. The averaging kernel is of expo…
A posteriori Error Estimates for Numerical Solutions to Hyperbolic Conservation Laws
Alberto Bressan, Maria Teresa Chiri, Wen Shen
The paper is concerned with a posteriori error bounds for a wide class of numerical schemes, for hyperbolic conservation laws in one space dimension. These estimates ar…
A Posteriori Error Estimates for Self-Similar Solutions to the Euler Equations
Alberto Bressan, Wen Shen
The main goal of this paper is to analyze a family of "simplest possible" initial data for which, as shown by numerical simulations, the incompressible Euler equations have multipl…
On Traffic Flow with Nonlocal Flux: a Relaxation Representation
Alberto Bressan, Wen Shen
We consider a conservation law model of traffic flow, where the velocity of each car depends on a weighted average of the traffic density ahead. The averaging kernel is of expo…
Stationary Wave Profiles for Nonlocal Particle Models of Traffic Flow on Rough Roads
Jereme Chien, Wen Shen
We study a nonlocal particle model describing traffic flow on rough roads. In the model, each driver adjusts the speed of the car according to the condition over an interval in the…
Vanishing Viscosity Solutions for Conservation Laws with Regulated Flux
Alberto Bressan, Graziano Guerra, Wen Shen
In this paper we introduce a concept of "regulated function" of two variables, which reduces to the classical definition when is independent of . We then consider a…
Backward Euler Approximations for Conservation Laws with Discontinuous Flux
Graziano Guerra, Wen Shen
Solutions to a class of conservation laws with discontinuous flux are constructed relying on the Crandall-Liggett theory of nonlinear contractive semigroups~\cite{CL}. In particula…
Global Riemann Solvers for Several Systems of Conservation Laws with Degeneracies
Wen Shen
We study several systems of conservation laws, arising in modeling of two phase flow with rough porous media and traffic flow with rough road condition. These systems s…
Growth Models for Tree Stems and Vines
Alberto Bressan, Michele Palladino, Wen Shen
The paper introduces a PDE model for the growth of a tree stem or a vine. The equations describe the elongation due to cell growth, and the response to gravity and to external obst…
Existence and Stability of Traveling Waves for an Integro-differential Equation for Slow Erosion
Graziano Guerra, Wen Shen
We study an integro-differential equation that describes the slow erosion of granular flow. The equation is a first order non-linear conservation law where the flux function includ…
An Integro-Differential Conservation Law arising in a Model of Granular Flow
D. Amadori, W. Shen
We study a scalar integro-differential conservation law. The equation was first derived in [2] as the slow erosion limit of granular flow. Considering a set of more general erosion…