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Research Output 1996 2019

  • 241 Citations
  • 10 h-Index
  • 34 Article
  • 2 Chapter
2019
Traffic Flow
Rough
Nonlocal Delay
Model
Discontinuous Coefficients

Traveling waves for conservation laws with nonlocal flux for traffic flow on rough roads

Shen, W., Dec 1 2019, In : Networks and Heterogeneous Media. 14, 4, p. 709-732 24 p.

Research output: Contribution to journalArticle

Open Access
Traffic Flow
Traveling Wave
Conservation Laws
Rough
Conservation
3 Citations (Scopus)

Traveling waves for nonlocal models of traffic flow

Ridder, J. & Shen, W., Jul 2019, In : Discrete and Continuous Dynamical Systems- Series A. 39, 7, p. 4001-4040 40 p.

Research output: Contribution to journalArticle

Open Access
Traffic Flow
Traveling Wave
Railroad cars
Model
Integrodifferential equations

Vanishing viscosity and backward Euler approximations for conservation laws with discontinuous flux

Guerra, G. & Shen, W., Jan 1 2019, In : SIAM Journal on Mathematical Analysis. 51, 4, p. 3112-3144 33 p.

Research output: Contribution to journalArticle

Discontinuous Flux
Vanishing Viscosity
Conservation Laws
Euler
Conservation
2 Citations (Scopus)

Vanishing viscosity solutions for conservation laws with regulated flux

Bressan, A., Guerra, G. & Shen, W., Jan 5 2019, In : Journal of Differential Equations. 266, 1, p. 312-351 40 p.

Research output: Contribution to journalArticle

Triangular Systems
Vanishing Viscosity
Systems of Conservation Laws
Discontinuous Functions
Scalar Conservation Laws
2018
2 Citations (Scopus)
Riemann Solvers
Systems of Conservation Laws
Conservation
Eigenvalues and eigenfunctions
Two phase flow
3 Citations (Scopus)

Traveling wave profiles for a Follow-the-Leader model for traffic flow with rough road condition

Shen, W., Sep 1 2018, In : Networks and Heterogeneous Media. 13, 3, p. 449-478 30 p.

Research output: Contribution to journalArticle

Traffic Flow
Traveling Wave
Rough
Discontinuous Differential Equations
Discontinuous Flux
4 Citations (Scopus)

Traveling waves for a microscopic model of traffic flow

Shen, W. & Shikh-Khalil, K., May 2018, In : Discrete and Continuous Dynamical Systems- Series A. 38, 5, p. 2571-2589 19 p.

Research output: Contribution to journalArticle

Traffic Flow
Traveling Wave
Railroad cars
Existence and Uniqueness of Solutions
Two-point Boundary Value Problem
2017

Feedback Stabilization of Stem Growth

Ancona, F., Bressan, A., Glass, O. & Shen, W., Dec 27 2017, (Accepted/In press) In : Journal of Dynamics and Differential Equations. p. 1-28 28 p.

Research output: Contribution to journalArticle

Feedback Stabilization
Elongation
Gravity
Stabilization
Vertical
2 Citations (Scopus)

Growth models for tree stems and vines

Bressan, A., Palladino, M. & Shen, W., Aug 15 2017, In : Journal of Differential Equations. 263, 4, p. 2280-2316 37 p.

Research output: Contribution to journalArticle

Growth Model
Operator Splitting
Elastic Deformation
Curl
State Constraints
5 Citations (Scopus)
Vanishing Viscosity
Flooding
Viscosity Solutions
Cauchy Problem
Polymers
2016
3 Citations (Scopus)

Global Riemann solver and front tracking approximation of three-component gas floods

Khorsandi, S., Shen, W. & Johns, R. T., Jan 1 2016, In : Quarterly of Applied Mathematics. 74, 4, p. 607-632 26 p.

Research output: Contribution to journalArticle

Front Tracking
Riemann Solver
Conservation
Hydrodynamics
Thermodynamics
3 Citations (Scopus)

On the Cauchy problems for polymer flooding with gravitation

Shen, W., Jul 5 2016, In : Journal of Differential Equations. 261, 1, p. 627-653 27 p.

Research output: Contribution to journalArticle

Flooding
Gravitation
Cauchy Problem
Polymers
Fluxes
2015
2 Citations (Scopus)

Slow erosion with rough geological layers

Shen, W., Jan 1 2015, In : SIAM Journal on Mathematical Analysis. 47, 4, p. 3116-3150 35 p.

Research output: Contribution to journalArticle

Erosion
Rough
Jump
Discontinuous Flux
Kink
2014
3 Citations (Scopus)

A semigroup approach to an integro-differential equation modeling slow erosion

Bressan, A. & Shen, W., Oct 1 2014, In : Journal of Differential Equations. 257, 7, p. 2360-2403 44 p.

Research output: Contribution to journalArticle

Balance Laws
Granular Flow
Integrodifferential equations
Erosion
Integro-differential Equation
7 Citations (Scopus)

Existence and stability of traveling waves for an integro-differential equation for slow erosion

Guerra, G. & Shen, W., Jan 1 2014, In : Journal of Differential Equations. 256, 1, p. 253-282 30 p.

Research output: Contribution to journalArticle

Integrodifferential equations
Erosion
Integro-differential Equation
Traveling Wave
Conservation Laws
2013
11 Citations (Scopus)

A multidimensional optimal-harvesting problem with measure-valued solutions

Bressan, A., Coclite, G. M. & Shen, W., Jul 8 2013, In : SIAM Journal on Control and Optimization. 51, 2, p. 1186-1202 17 p.

Research output: Contribution to journalArticle

Measure-valued Solutions
Optimal Harvesting
Cost functions
Elliptic Equations
Boundary conditions
2012
21 Citations (Scopus)

An integro-differential conservation law arising in a model of granular flow

Amadori, D. & Shen, W., Mar 1 2012, In : Journal of Hyperbolic Differential Equations. 9, 1, p. 105-131 27 p.

Research output: Contribution to journalArticle

Granular Flow
Erosion
Conservation Laws
Fractional Step Method
Bounded variation
11 Citations (Scopus)

Erosion Profile by a Global Model for Granular Flow

Shen, W. & Zhang, T., Jun 1 2012, In : Archive for Rational Mechanics and Analysis. 204, 3, p. 837-879 43 p.

Research output: Contribution to journalArticle

Granular Flow
Erosion
Entropy
Kink
Weak Solution
10 Citations (Scopus)

Front tracking approximations for slow erosion

Amadori, D. & Shen, W., May 1 2012, In : Discrete and Continuous Dynamical Systems. 32, 5, p. 1481-1502 22 p.

Research output: Contribution to journalArticle

Front Tracking
Entropy Solution
Erosion
Approximate Solution
Entropy
4 Citations (Scopus)

Lipschitz semigroup for an integro-differential equation for slow erosion

Colombo, R. M., Guerra, G. & Shen, W., Dec 20 2012, In : Quarterly of Applied Mathematics. 70, 3, p. 539-578 40 p.

Research output: Contribution to journalArticle

Front Tracking
Granular Flow
Integrodifferential equations
Erosion
Nonlinear Partial Differential Equations
3 Citations (Scopus)

Variational analysis of nash equilibria for a model of traffic flow

Bressan, A., Liu, C. J., Shen, W. & Yu, F., Dec 20 2012, In : Quarterly of Applied Mathematics. 70, 3, p. 495-515 21 p.

Research output: Contribution to journalArticle

Variational Analysis
Traffic Flow
Nash Equilibrium
Driver
Equilibrium Solution
2011
3 Citations (Scopus)

Measure-valued solutions to a harvesting game with several players

Bressan, A. & Shen, W., Jan 1 2011, Annals of the International Society of Dynamic Games. Birkhauser, p. 399-423 25 p. (Annals of the International Society of Dynamic Games; vol. 11).

Research output: Chapter in Book/Report/Conference proceedingChapter

Measure-valued Solutions
Harvesting
Game
Optimal Harvesting
Second Order ODE
10 Citations (Scopus)

The Slow Erosion Limit in a Model of Granular Flow

Amadori, D. & Shen, W., Jan 1 2011, In : Archive for Rational Mechanics and Analysis. 199, 1, p. 1-31 31 p.

Research output: Contribution to journalArticle

Granular Flow
Erosion
Avalanche
Granular materials
Boundary value problems
2009
15 Citations (Scopus)

Global existence of large BV solutions in a model of granular flow

Amadori, D. & Shen, W., Sep 1 2009, In : Communications in Partial Differential Equations. 34, 9, p. 1003-1040 38 p.

Research output: Contribution to journalArticle

Granular Flow
Global Existence
Entropy
Linearly
Granular Matter

Non-cooperative and semi-cooperative differential games

Shen, W., Jan 1 2009, Annals of the International Society of Dynamic Games. Birkhauser, p. 85-104 20 p. (Annals of the International Society of Dynamic Games; vol. 10).

Research output: Chapter in Book/Report/Conference proceedingChapter

Cooperative Game
Differential Games
Nash Equilibrium
Non-cooperative Game
Equilibrium Solution
2008
9 Citations (Scopus)

On the shape of avalanches

Shen, W., Mar 15 2008, In : Journal of Mathematical Analysis and Applications. 339, 2, p. 828-838 11 p.

Research output: Contribution to journalArticle

Avalanche
Granular Matter
Balance Laws
Catastrophe
Dimensionless
1 Citation (Scopus)

Vanishing viscosity approximation to hyperbolic conservation laws

Shen, W. & Xu, Z., Apr 1 2008, In : Journal of Differential Equations. 244, 7, p. 1692-1711 20 p.

Research output: Contribution to journalArticle

Viscosity Approximation
Vanishing Viscosity
Higher Order Approximation
Hyperbolic Conservation Laws
Shock
2006

Optimal tracing of viscous shocks in solutions of viscous conservation laws

Wen, S. & Mee, R. P., Dec 1 2006, In : SIAM Journal on Mathematical Analysis. 38, 5, p. 1474-1488 15 p.

Research output: Contribution to journalArticle

Viscous Conservation Laws
Tracing
Shock
Conservation
Scalar Conservation Laws
2005
22 Citations (Scopus)

Small BV solutions of hyperbolic noncooperative differential games

Bressan, A. & Shen, W., Mar 9 2005, In : SIAM Journal on Control and Optimization. 43, 1, p. 194-215 22 p.

Research output: Contribution to journalArticle

Non-cooperative Game
Differential Games
Conservation
Feedback
n-tuple
2004
25 Citations (Scopus)

Semi-cooperative strategies for differential games

Bressan, A. & Shen, W., Jan 1 2004, In : International Journal of Game Theory. 32, 4, p. 561-593 33 p.

Research output: Contribution to journalArticle

Differential Games
Nash Equilibrium
Value Function
Viscosity Approximation
Pareto Optimum
2000
15 Citations (Scopus)

BV estimates for multicomponent chromatography with relaxation

Bressan, A. & Shen, W., 2000, In : Discrete and Continuous Dynamical Systems. 6, 1, p. 21-38 18 p.

Research output: Contribution to journalArticle

Chromatography
Lipschitz
Liquid
Estimate
Balance Laws
1999
1 Citation (Scopus)
Scalar Conservation Laws
Semi-implicit
Source Terms
Finite Difference Scheme
Error Bounds
6 Citations (Scopus)

On the zero relaxation limit for a system modeling the motions of a viscoelastic solid

Shen, W., Tveito, A. & Winther, R., Jan 1 1999, In : SIAM Journal on Mathematical Analysis. 30, 5, p. 1115-1135 21 p.

Research output: Contribution to journalArticle

Relaxation Limit
System Modeling
Motion
Zero
Conservation
1998
27 Citations (Scopus)

Uniqueness for discontinuous ODE and conservation laws

Bressan, A. & Shen, W., Dec 1 1998, In : Nonlinear Analysis, Theory, Methods and Applications. 34, 5, p. 637-652 16 p.

Research output: Contribution to journalArticle

Theorem proving
Theorem Proving
Well-posedness
Conservation Laws
Integral equations
1996
5 Citations (Scopus)

A system of conservation laws including a stiff relaxation term; The 2D case

Shen, W., Tveito, A. & Winther, R., Jan 1 1996, In : BIT Numerical Mathematics. 36, 4, p. 786-813 28 p.

Research output: Contribution to journalArticle

Systems of Conservation Laws
Relaxation Time
Relaxation time
Error Bounds
Conservation