Publications of Wen Shen
Textbook

An Introduction to Numerical Computation. World
Scientific Publishing. 2016. (250 pages)
Here is an errata for the book.
Some Research Papers in Journals
 (43). Wen Shen.
Traveling Waves for Conservation Laws with Nonlocal Flux for Traffic Flow on Rough Roads
Preprint 2018. Submitted.
[ Preprint on ArXiv. ]
 (42). Johanna Ridder and Wen Shen.
Traveling Waves for Nonlocal Models of Traffic Flow
Preprint 2018, Submitted.
[ Preprint on ArXiv. ]
 (41). Alberto Bressan, Graziano Guerra and Wen Shen.
Vanishing Viscosity Solutions for Conservation Laws with Regulated Flux.
Journal of Differential Equations 266 (2019) 312351.
[ a pdffile.]
 (40). Graziano Guerra and Wen Shen.
Backward Euler Approximations for Conservation Laws with Discontinuous Flux.
Preprint 2018, submitted. (24 pp)
[ a pdffile.]
 (39). Wen Shen.
Traveling Wave Profiles for a FollowtheLeader Model for Traffic Flow with Rough Road Condition.
Netw. Heterog. Media 13 (2018), no. 3, 449478.
[ a pdffile.]
 (38).
Fabio Ancona, Alberto Bressan, Olivier Glass, Wen Shen.
Feedback Stabilization of Stem Growth.
JDDE (Journal of Dynamical Differential Equations) 2017.
Online first at: https://doi.org/10.1007/s108840179633z
[ a pdffile.]
 (37). Wen Shen and Karim ShikhKhalil.
Traveling Waves for a Microscopic Model of Traffic Flow.
Discrete and Continuous Dynamical System 38 (2018), no. 5, 25712589.
[ a pdffile.]
 (36). Wen Shen.
Global Riemann Solvers for Several 3x3 Systems of Conservation Laws with Degeneracies.
Math. Models Methods Appl. Sci. 28 (2018), no. 8, 15991626.
[ a pdffile. ]
 (35). A. Bressan, M. Palladino, W. Shen.
Growth Models for Tree Stems and Vines.
J. Differential Equations 263 (2017), no. 4, 22802316.
[ a pdffile. ]
 (34). Wen Shen ,
On the Uniqueness of Vanishing Viscosity Solutions for Riemann Problems for Polymer Flooding.
NoDEA Nonlinear Differential Equations Appl. 24 (2017), no. 4, Art. 37, 25 pages.
The Special Issue for 60th Birthday of Alberto Bressan.
[ a pdffile]
 (33). Graziano Guerra and Wen Shen ,
Vanishing Viscosity Solutions of Riemann Problems for Models of Polymer Flooding.
In Nonlinear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis. The Helge Holden Anniversary Volume. European Mathematical Society, Congress Reports (2018), pp 261285. Editors: F. Gesztesy, H. HancheOlsen, E. Jakobsen, Y. Lyubarskii, N. Risebro, and K. Seip.
[ a pdffile]
 (32). Wen Shen,
On the Cauchy Problems for Polymer Flooding with Gravitation,
Journal of Differential Equations, 261 (2016), 627653.
[ a pdffile ]
 (31). Saeid Khorsandi, Wen Shen and Russell
T. Johns,
Global Riemann Solver and Front Tracking Approximation of ThreeComponent Gas Floods.
Quarterly of Applied Mathematics, Brown University, vol LXXIV, Nr 4, pp. 607632. (2016)
[ a pdffile ]
 (30). Wen Shen,
Slow Erosion with Rough Geological Layers.
SIAM Journal of Mathematical Analysis, 47 (2015), no. 4, pp. 31163150.
[ a pdffile ]
 (29). Alberto Bressan and Wen Shen,
A Semigroup Approach to an IntegroDifferential Equation Modeling Slow Erosion.
Journal of Differential Equations, 257 (2014), no. 7, 23602403.
[ a pdffile ]
 (28). Graziano Guerra and Wen Shen,
Existence and Stability of Traveling Waves for an Integrodifferential Equation for Slow Erosion.
J. Differential Equations, 256 (2014), pp. 253282.
[ a pdffile ]
 (27). A. Bressan, J. Liu, W. Shen and F. Yu.
Variational Analysis of Nash Equilibria for a Model of Traffic Flow
Quarterly of Applied Mathematics, Brown University, Vol LXX, No. 3, the special issue in honor of Dafermos' 70th birthday, (2012), pp. 495515.
[ a pdffile ]

(26). R. Colombo, G. Guerra and W. Shen,
Lipschitz Semigroup for an IntegroDifferential Equation for Slow Erosion
Quarterly of Applied Mathematics, Brown University, Vol LXX, No. 3, the special issue in honor of Dafermos' 70th birthday, (2012) pp. 539578.
[ a pdffile ]
 (25). A. Bressan, G. M. Coclite, and
W. Shen,
A Multidimensional Optimal Harvesting Problem with Measure Valued Solutions.
SIAM J. Control Optim. 51 (2013). no.2, 11861202.
[ a pdffile ]
 (24). Debora Amadori and Wen Shen,
An IntegroDifferential Conservation Law arising in a Model of Granular Flow.
Journal of Hyperbolic Differential Equations, Vol 9, Issue 1, March 2012, pp. 105131.
DOI: 10.1142/S0219891612500038
[ a pdffile ]
 (23). Wen Shen and Tianyou Zhang,
Erosion Profile by a Global Model for Granular Flow.
Arch. Rational Mech. Anal. Vol 204, Nr 3, pp 837879, (2012).
DOI: 10.1007/s0020501204992
[ a pdffile ]
 (22). Debora Amadori and Wen Shen,
Front Tracking Approximations for Slow Erosion.
Discrete and Continuous Dynamical Systems, Vol 32, Nr 5, May 2012, pp. 14811502.
DOI: 10.3934/dcds.2012.32.1481
[ a pdffile ]
 (21). Debora Amadori and Wen Shen
Mathematical Aspects of a Model for Granular Flow,
In ``IMA Volumes in Mathematics and its Applications'', vol. 153, ``Nonlinear Conservation Laws and Applications'', pp. 169180. Springer, 2011. Editors: A. Bressan, GQ. Chen, M. Lewicka and D. Wang,
[ a pdffile ]
 (20). Debora Amadori and Wen Shen
A Hyperbolic Model of Granular Flow,
In H. Holden and K. H. Karlsen, editors, "Nonlinear Partial Differential Equations", Contemp. Math. Amer. Math. Soc., vol 526, p.118. (2010)
[ a pdffile ]
 (19). Debora Amadori and Wen Shen
Slow Erosion Limit in Model of Granular Flow.
Archive for Rational Mechanics an Analysis, 199 p. 131 (2011).
[ a pdffile ]
 (18). Alberto Bressan and Wen Shen
Measure Valued Solutions to a Harvesting Game with Several Players.
In M. Breton and K. Szajowski (eds.) "Advances in Dynamic Games", Annals of the International Society of Dynamic Games, vol 11, pp.399423. Springer, 2011.
[a pdffile]
 (17). Debora Amadori and Wen Shen,
Global Existence of Large BV Solutions in a Model of Granular Flow.
Comm PDE, 34 (2009), n0. 79, 10031040.
[ a pdffile ]
 (16). Wen Shen,
NonCooperative and SemiCooperative Differential Games,
in "Advances in Dynamic Games and their Applications; Analytical and Numerical Developments". Series: Annals of ISDG (International Symposium of Dynamical Games)}, vol. 10. Editors: Pierre Bernhard, Gaitsgory Vladimir, Odile Pourtallier. Birkehauser (2009). pp. 85106.
[ a pdffile ]
 (15). Alberto Bressan and Wen Shen,
Measure Valued Solutions for a Differential Game Related to Fish Harvesting.
SIAM J. Control and Optimization, Volume 47, Issue 6, pp. 31183137 (2009) .
[ a pdf file ].
 (14). Wen Shen,
On the Shape of Avalanche.
J. Math Anal. Appl. 339 (2008) 828838.
[ a pdf file ].
 (13). Wen Shen and Zhengfu Xu,
Vanishing Viscosity Approximation to Hyperbolic Conservation Laws.
Journal of Differential Equations, 244(2008) 16971711.
[ a pdffile ].
 (12). A. Bressan and W. Shen,
Optimality Conditions for Solutions to Hyperbolic Balance Laws
In ``Control Methods in PDE and Dynamical Systems'', F.~Ancona and R.~Triggiani eds., AMS Contemporary Mathematics Series 426, pp 129152, 2007.
[ a pdffile ]
 (11). A. Bressan and W. Shen,
Unique Solutions of Discontinuous O.D.E.'s in Banach Spaces,
Analysis and Applications, Vol. 4, No. 3 (2006) 247262.
[ a pdffile. ]
 (10). W. Shen and M. Park,
Optimal Tracing of Viscous Shocks in Solutions of Viscous Conservation Laws,
SIAM J. Math.Anal. vol. 38, No. 5, (2007) pp.14741488.
[ a pdffile .]
 (9). A. Bressan and W. Shen,
Semicooperative Strategies for Differential Games,
International Journal of Game Theory, Vol 32, No 4, (2004), pp. 561593.
[ pdffile . ]
 (8). A. Bressan and W. Shen,
Small BV Solutions of Hyperbolic Noncooperative Differential Games,
SIAM J. Control and Optimization, Vol. 43, No. 1, pp. 104215, 2004
[pdffile.]
 (7). A. M. Bruaset, X. Cai, H. P. Langtangen, G. T. Lines,
K. Samuelsson, W. Shen, A. Tveito, G. Zumbusch,
Performance modeling of PDE solvers.
In H. P. Langtangen and A. Tveito, editors, Advanced Topics in Computational Partial Differential Equations  Numerical Methods and Diffpack Programming.
pp. 361399, Springer, 2003.
[ pdffile.]
 (6). A. Bressan and W. Shen,
BV estimate for multicomponent chromatography with relaxation,
Discrete and Continuous Dynamical Systems, The Millennium Issue, 6 (2000), pp. 2138.
[ pdffile.]
 (5). A. Bressan, W. Shen,
On Discontinuous Differential Equation,
Differential Inclusions and Optimal Control, Lecture Notes in Nonlinear Analysis, Vol. 2, 1998, pp. 7387.
[ pdffile]
 (4). W. Shen, A. Tveito and R. Winther,
On the zero relaxation limit for a system modeling the motions of a viscoelastic solid,
SIAM J. Math. Anal. Vol. 30, No. 5, pp. 11151135, 1999.
[ a pdf file. ]
 (3). A. Bressan, W. Shen,
Uniqueness for discontinuous ODEs and conservation laws
Nonlinear Analysis, Theory, Methods, and Applicatipns, 34 (1998) pp. 637652.
[ a pdf file.]
 (2). W. Shen,
Error bounds of finite difference schemes for twodimensional scalar conservation with source terms,
IMA Journal of Numerical Analysis, vol. 19, pp. 7789, 1999.
[ a pdffile ]
 (1). W. Shen, A. Tveito and R. Winther,
A system of conservation laws including a stiff relaxation term; the 2D case,
BIT, 36:4(1996), pp. 786813.
[ a pdffile]
Proceeding Papers
 (8). Debora Amadori, Rinaldo Colombo, Graziano
Guerra and Wen Shen,
SLOW EROSION OF GRANULAR FLOW: CONTINUOUS AND DISCONTINUOUS PROFILES.
Submitted to the proceedings of HYP 2012, Padova, Italy.
[ a pdffile ]
 (7). Wen Shen and Tianyou Zhang,
A Global Scalar Conservation Law for Erosion Profiles.
In the Proceedings of HYP 2010, Beijing. Editors:T. Li and S. Jiang. p. 675682. Series in Comtemporary Applied Mathematics CAM 17, Higher Education Press, 2012.
[ a pdffile ]
 (6). Debora Amadori and Wen Shen,
A Nonlocal Conservation Law from a Model of Granular Flow.
In the Proceedings of HYP 2010, Beijing. Editors:T. Li and S. Jiang. p. 265272. Series in Comtemporary Applied Mathematics CAM 17, Higher Education Press, 2012.
[ a pdffile ]
 (5). W.Shen,
On a Model of Granular Flow.
In "Hyperbolic Problems: Theory, Numerics and Applications", Proceedings of the 12th International Conference on Hyperbolic Problems held in University of Maryland, College Park, USA, June 913 2008. Eds: Eitan Tadmor, Jian Guo Liu, Athanasios Tzavaras. AMS 2009, p. 939948.
[a pdffile]
 (4). W. Shen,
Finite Dimensional Representation of Solutions of Viscous Conservation Laws
in "Hyperbolic Problems: Theory, Numerics, Applications", Proceeding of HYP2006 in Lyon, France. S. BenzoniGavage and D. Serre editors. Springer 2008. pp 981988.
[ a pdffile ].
 (3). A. Bressan and W. Shen,
Noncooperative Differential Games,
in "Hyperbolic Problems: Theory, Numerics, Applications", Proceeding of HYP2004 in Osaka. F. Asakura, chief editor, Yokohama Publishers, pp. 7784, 2006.
[a pdf file]
 (2). A. Bressan and W. Shen,
The convergence of Multicomponent chromatography with relaxation
in "Hyperbolic Problems: Theory, Numerics, Applications", Proceedings of HYP2000 in Magdeburg. H.Freistuehler and G. Warnecke eds., Birkhauser Verlag, Basel, pp. 197205, 2001.
[ a pdf file ].
 (1). W. Shen, A. Tveito and R. Winther,
Rate of convergence for the zero relaxation limit.
``Hyperbolic Problems: Theory, Numerics, Applications'', the proceedings of the 7th Int. Conf. on Hyperbolic Problems. Editors: M.~Fey and R.~Jeltsch, International Series of Numerical Mathematics, Vol. 130, pp.~865874, Birhauser Verlag Basel, Switzerland, 1999.
[a pdf file.]
Thesis:
 (2). W. Shen,
Hyperbolic Conservation Laws with Relaxation Terms,
PhD. Thesis, Department of Informatics, University of Oslo, Norway. March 30, 1998.
 (1). Wen Shen,
Numerical Solution of the Pressure Equation in a Simple Model of Aluminium DCcasting,
Thesis for Cand. Scient. Degree, Institute of Informatics, University of Oslo, and Section for Applied Mathematics, SINTEF, Oslo, Norway, April 1994.
[ a compressed postscript file, 748675 bytes ]
Research reports:
 (5). A.M. Bruaset, X. Cai, H.P. Langtangen, G.T. Lines,
K. Samuelsson, W. Shen, A. Tveito and G. Zumbusch,
CPUmeasurements of some numerical PDE simulations,
Technical report, Preprint 19983, Department of Informatics, University of Oslo, Norway.
 (4). Wen Shen,
A comparison between two finite element methods for the solution of a simplified model of alloy casting,
Research Report, ISBN 8273681211, ISSN 08063036, December 1995, Department for Informatics, University of Oslo, Norway.
[ a compressed postscript file, 418876 bytes ]
 (3). H. Thevik, A. Mo, W. Shen,
Todimensjonale strøminingseffekter ved utsvetting under DCstøping,
SINTEFreport no. STF24 F94064, 1994. Section for Applied Mathematics, SINTEF, Oslo, Norway. (In Norwegian.)
 (2). H. P. Langtangen, G. Pedersen and W. Shen,
Finite Element Preprocessors in Diffpack,
SINTEFreport no. STF33 A94051 (1994).
[ a pdffile . ]
 (1). W. Shen, A. M. Bruaset,
Mixed Finite Element Solution of Elliptic Boundary Value Problems,
SINTEFreport no. STF33 A94018, 1994.
[a compressed postscript file, 337657 bytes ]
Wen Shen.