# Publications of Li Chen

1. L. Chen, H. Siedentop Blow-Up of Solutions to the Patlak-Keller-Segel Equation in Dimension $\nu\geq2$, Applied Mathematics Letters, 2017.
2. J. Che,  L. Chen,  S. G\"otlich,  A. Pandey, and J. Wang, Boundary layer analysis from the Keller-Segel system to the aggregation system in one space dimension, Comm. Pure. Appl. Anal. 16 (2017), 1013-1036
3. L. Chen, S. G\"ottlich, and Q. Yin, Mean Field Limit and Propagation of Chaos for a Pedestrian Flow Model, J. Statistical Physics, 166 (2017), 211-229.
4. S. Bian, L. Chen, and E. Latos, Global existence and asymptotic behavior of solutions to a nonlocal Fisher-KPP type problem. Nonlinear Anal. 149 (2017), 165-176.
5. J. Che, L. Chen, B. Duan and Z. Luo, On the existence of local strong solutions to chemotaxis-shallow water system with large data and vacuum, accepted by  J. Diff. Equs, (2016).
6. S. Bian and L. Chen, A nonlocal reaction diffusion equation and its relation with Fujita exponent, Journal of Mathematical Analysis and Applications, 444 (2016) 1479-1489.
7. J. Che, L. Chen, S. Göttlich and J. Wang, Existence of a Classical Solution to Complex Material Flow Problems, Mathematical Methods in the Applied Sciences, 39(14) (2016) 4069-4081.
8. J. Wang, L. Chen and L. Hong, parabolic elliptic type Keller-Segel system on the whole space case, Discrete and continuous dynamical systems, V. 36, No. 2, 2016.
9. L. Chen and J. Wang, Exact Criterion for Global Existence and Blow Up to a Degenerate Keller-Segel System, Documenta Mathematica, 19, (2014), 103-120.
10. R. Yang and L. Chen, Mean-Field Limit for a Collision-Avoiding Flocking System and the Time-Asymptotic Flocking Dynamics for the Kinetic Equation, Kinetic and related models, 7-2, (2014), 381-400.
11. L. Chen, D. Donatelli and P. Marcati, Incompressible type limit analysis of a hydrodynamic model for charge-carrier transport, SIAM Math. Anal. 45 (2013), no.3, 915-933.
12. L. Chen and H. Siedentop, Positivity of jpjajqjb+jqjbjpja, J. Funct. Anal. 264 (2013), no. 12, 2817-2824.
13. S. Bian, L. Chen and M. Dreher, Boundary layer analysis in the semiclassical limit of a quantum drift diffusion model, J. Diff. Eqns, 253, (2012), 356-377.
14. L. Chen, J.-G. Liu and J. Wang, Multi-dimensional degenerate Keller-Segel system with critical diffusion exponent 2n=(n + 2), V. 44, No.2, SIAM Math. Anal., (2012)1077-1102.
15. J. A. Carrillo, L. Chen, J.-G. Liu and J. Wang, A Note on the Subcritical Two Dimensional Keller-Segel System, Acta Appl Math, V. 119, Issue 1, (2012), 43-55.
16. L. Chen, Ji Oon Lee and B. Schlein, Rate of Convergence Towards Hartree Dynamics, J. Stat. Phys., (2011) 144:872-903.
17. G. Ali and L. Chen, The zero-electron-mass limit in the Euler-Poisson system for both well and ill prepared initial data, Nonlinearity, 24 (2011), 2745-2761.
18. L. Chen, X. Chen and A. J¨ungel, Semiclassical limit in a simplified quantum energy transport model for semiconductors, Kinetic and Related Models, 4-4 December (2011), 1049-1062.
19. L. Chen and Ji Oon Lee, Rate of convergence in nonlinear Hartree dynamics with factorized initial data, J. Math. Phys. 52, 052108, (2011).
20. L. Chen and M. Dreher, Viscous quantum hydrodynamics and parameter-elliptic systems. Math. Meth. Appl. Sci., 34, (2011), 520-531. 4.
21. X. Chen, L. Chen and C. Sun, A six order parabolic system in semiconductors, Chin. Ann. Math. Ser. B 32 (2011), no. 2, 265-278.
22. L. Chen and M. Dreher, Quantum semiconductor models, Partial Differential Equations and Spectral Theory, Series: Operator Theory: Advances and Applications, (2011), 1-72.
23. L. Chen, X. Chen and C. Zhang, Vanishing electron mass limit in the bipolar Euler-Poisson system. Nonlinear Anal. Real World Appl. 12 (2011), no. 2, 1002-1012.
24. L. Chen, The zero-electron-mass limit in the hydrodynamic model (Euler-Poisson system), Some problems on nonlinear hyperbolic equations and applications, Series in Contemporary Applied Mathematics CAM15, , Higher Education Press, 2010.
25. G. Ali, L. Chen, A. J¨ungel, and Y.-J. Peng. The zero-electron-mass limit in the hydrodynamic model for plasmas. Nonlin. Anal. 72 (2010), 4415-4427.
26. X. Chen, L. Chen, H. Jian, Existence, Semiclassical Limit and Long-time Behavior of Weak Solution to Quantum Drift-diffusion Model, Nonlinear Analysis Series B: Real World Applications, 10 (2009) 1321-1342.
27. X. Chen, L. Chen, The bipolar quantum drift-diffusion model, Acta Mathematica Sinica, English Series,Vol. 25, No. 4, (2009), 617-638.
28. Q. Ju, L. Chen, Semiclassical limit for bipolar quantum drift-diffusion model, Atca Mathematica Scientia. (2009) ,29B(2):285-293.
29. X. Chen, L. Chen, H. Jian, The Dirichlet problem of Quantum Drift-diffusion Model, Nonlinear Anal. Series A: Theory, Methods and Applications, 69 (2008), 3084–3092.
30. L. Chen, Q. Ju, The semiclassical limit in the quantum drift-diffusion equations with isentropic pressure, Chin. Ann. Math. 29B(4), (2008) , 369-384.
31. L. Chen, X. Chen, Dirichlet-Neumann problem for unipolar isentropic quantum driftdiffusion model, Tsinghua Science and Technology, V. 13(4), (2008), 560-569.
32. X. Chen, L. Chen, Initial time layer problem for quantum drift-diffusion model, J. Math. Anal. Appl. 343 (2008), no. 1, 64–80.
33. X. Chen, L. Chen, H. Jian, The Existence and Long-Time Behavior of Weak Solution to Bipolar Quantum Drift-Diffusion Model, Chinese Annals of Mathematics-Series B, V. 28, No. 6,(2007),651-664.
34. L. Chen, M. Dreher, The viscous model of quantum hydrodynamics in several  dimensions, Mathematical Models and Methods in Applied Sciences, Vol. 17, No. 7 (2007) 1065-1093.
35. L. Chen, A. Juengel, Analysis of a Parabolic Cross-Diffusion Semiconductor Model with Electron-Hole Scattering, Comm. PDE, 32: (2007), 127-148.
36. L. Chen, L. Hsiao, G. Warnecke, Study on a Cross Diffusion Parabolic System, Acta Math. Appl. Sin. Engl. Ser. 23 (2007), no. 1, 9–28.
37. L. Chen, Q. Ju, Existence of weak solution and semiclassical limit for quantum driftdiffusion model, Zeitschrift f¨ur Angewandte Mathematik und Physik, V. 58, No.1, (2007), 1-15.
38. L. Chen, A. Juengel, Analysis of a parabolic cross-diffusion population model without self-diffusion, J. Diff. Eqs., 224 (2006), 39-59.
39. L. Chen, Mathematical analysis of a population dynamics system with strong crossdiffusion, Hyperbolic Problems, Theory, Numerics and Applications, Yokohama Publishers, (2006).
40. L. Chen, H. Liu, Generalized Solution of a Kind of Nonparametric Curvature Evolution with Boundary Condition, Acta Mathematica Sinica, V.22, No.2, (2006), 455-468.
41. L. Chen, L. Hsiao, Y. Li, Large Time Behavior and Energy Relaxation Time Limit of the Solutions to an Energy Transport Model in Semiconductors, J. Math. Anal. and Appl. 312 (2005), 596-619.
42. L. Chen, A. Juengel, Analysis of a multi-dimensional parabolic population model with strong cross-diffusion, SIAM J. Math. Anal., V.36, No.1, (2004), 301-322.
43. L. Chen, L. Hsiao, Y. Li, Global Existence and Asymptotic Behavior to the Solutions of 1-D Lyumkis Energy Transport Model for Semiconductors, Quart Appl. Math. V.62, No.2, (2004), 337-358.
44. L. Chen, L. Hsiao, Y. Li, Strong Solution to a Kind of Cross Diffusion Parabolic System, Comm. Math. Sci. V.1, No.4, (2003), 799-808.
45. L. Chen, L. Hsiao, The Solution of Lyumkis Energy Transport Model in Semiconductor Science, Math. Meth. Appl. Sci. 26, (2003), 1421-1433.
46. L. Chen, L. Hsiao, Energy Transport Model in Semiconductor Science, Acta Analysis functionalis applicata, V.5, No.1, (2003), 35-40.
47. L. Chen, Parabolic Type Monge-Ampere Equation with Zero Initial Boundary Value, Kumamoto J. of Math., V.16, (2003), 27-42.
48. L. Chen, G. Wang, Some remarks on the solution of one type of parabolic Monge- Ampere equation, (in Chinese) Chinese Ann. Math A. V.24, No.1, (2003), 33-40. (English version: Chinese Journal of Contemporary Mathematics, V.24, No.1, 2003)
49. Y. Li, L. Chen, Global Existence and Asymptotic Behavior to the solution of 1-D Energy Transport Model for Semiconductors, J. Partial Diff. Eqs. 15 (2002), 81-95.
50. L. Chen, G. Wang, S. Lian, Convex-monotone functions and generalized solution of parabolic Monge-Ampere equation, J. Diff. Eqns. 186, (2002), 558-571.
51. L. Chen, G. Wang, S. Lian, Generalized solution of the first boundary value problem for parabolic Monge-Ampere equation, J. Partial Diff. Eqs. 14 (2001), 149-162.
52. S. Lian, G. Wang, L. Chen, Remarks on a mathematical model from the theory of optimal investment, Northeast. Math. J. , 17 (2), (2001), 127-129.
53. L. Chen, Existence and uniqueness of generalized solution to parabolic Monge-Ampere equation, (in Chinese) Acta Scientiarum Naturalium Universitatis Jilinensis, No. 4, (2000), 1-9.
54. L. Chen, Interior estimates for generalized solutions of the parabolic Monge-Ampere equation, Northeast. Math. J. , 16 (4), (2000), 387-390.
55. L. Chen, G. Wang, Some remarks on one type of parabolic Monge-Amp`ere equation, Advances in Math.(China) 28. No. 4., (1999), 381-383.