Position: Research
Scientist in Partial Differential Equation
Email: renjun.duan@oeaw.ac.at
Tel.: +43-732-24685250
Fax:
+43-732-24685212
Address:
Johann Radon Institute for Computational and Applied
Mathematics (RICAM)
Altenbergerstrasse 69, A-4040 Linz, Austria
Curriculum
Vitae (full) pdf file
Educations
--PhD, Sep. 2005-Aug. 2008, City University of Hong Kong, Hong Kong
--MSc, Sep. 2002-Jul. 2005, Huazhong Normal University, China
Research Interests
I am interested in the theoretical study of partial differential
equations arising from Mathematical Physics and Biology such as fluid dynamics,
kinetic theory and chemotaxis. Research topics include the Boltzmann equation,
Navier-Stokes equations and mixed-type equations with relaxation. By using
tools from PDE and Functional Analysis, I try to understand well-posedness and
large-time behavior for the Cauchy problem or initial boundary value problem.
Academic Visits
--City University of Hong Kong, HK, Dec. 1-31, 2009
--University of Cambridge, UK, Oct. 26-Nov. 22, 2009
--Universitat Autonoma de Barcelona, Spain, Oct. 19-24, 2009
--University of Pavia, Italy, May 24-30, 2009.
--University of Cambridge, UK, Nov. 3-10, 2008.
--Universite de Rouen, France, Feb. 4-8, 2008.
--Institut de Recherche de l'Ecole navale, France, Jan. 7-Feb. 3, 2008.
--National Taiwan University, Taiwan, Jun. 15-Jul. 15, 2007.
Conferences
--Workshop “Theory and Numerics for Kinetic Equations”, Nov. 16-18, 2009,
Saarland University, Saarbrucken, Germany.
--Concentration en vitesse et en espace dans les modèles cinétiques et
diffusifs (chemotaxis, gravitation, swarming), Oct. 6-7, 2009, IHP and ENS,
Paris. pdf file
--CoLab Mathematics Summer School and Workshop on “Kinetics and
statistical methods for complex particle systems”, Jul. 13-24, 2009, Lisbon,
Portugal.
--PIMS/Accelerate Canada Summer School in PDE: Topics in Kinetic Theory,
Jun. 29-Jul. 3, 2009, University of Victoria, Canada.
--Modern Topics in Nonlinear Kinetic Equations, Apr. 20-22, 2009,
University of Cambridge, UK. pdf file
--International Conference on Kinetic and Related Models, Apr. 1-4,
2009, Wuhan University, China.
--Kinetic modelling for socio-economic and related problems, Nov. 27-29,
2008, Vigevano, Italy.
--Twelfth International Conference on “Hyperbolic Problems: Theory,
Numerics, Applications”, Jun. 9-13, 2008, University of Maryland, USA. pdf file
--Fourth Pacific Rim Conference on Mathematics, Dec. 7-11, 2007, City
University of Hong Kong, Hong Kong.
--Second Workshop on Nonlinear PDEs: Analysis, Computation and
Application, May 31-Jun. 2, 2007, Seoul National University, Korea.
--First PhD Student Workshop 2007 (Suzhou) City University of Hong Kong,
Apr. 10-11, 2007, China.
--International Conference on Conservation Laws & Kinetic equations,
Dec. 7-12, 2006, Shanghai Jiao Tong University, China. pdf file
Accepted and Published
Research Papers
1.
With R.M. Strain: Optimal time decay of the
Vlasov-Poisson-Boltzmann system in ${\mathbb{R}}^3$, accepted by Archive for Rational Mechanics and Analysis (Jan.
18, 2010). pdf file
2.
With K. Fellner and C.-J. Zhu: Energy method for
multi-dimensional balance laws with non-local dissipation, to appear in Journal Mathematiques Pures Appliquees
(2009). pdf file
3.
With T. Yang: Stability of the one-species
Vlasov-Poisson-Boltzmann system, SIAM
Journal on Mathematical Analysis, 41 (2010), no. 6, 2353-2387. pdf file
4.
Stability of the Boltzmann equation with potential
forces on torus, Physica D: Nonlinear
Phenomena 238 (2009), 1808-1820. pdf file
5.
With H.-F. Ma: Global existence and convergence
rates for the $3$-D compressible Navier-Stokes equations without heat
conductivity, Indiana University
Mathematics Journal 57 (2008), 2299-2320. pdf file
6.
With M.-R. Li and T. Yang: Propagation of
singularities in the solutions to the Boltzmann equation near equilibrium, Mathematical Models and Methods in Applied
Sciences 18 (2008), no. 7, 1093-1114. pdf file
7.
On the Cauchy problem for the Boltzmann equation in
the whole space: Global existence and uniform stability in $L^2_x(H^N_x)$, Journal of Differential Equations 244
(2008), no. 12, 3204-3234. pdf
file
8.
With S. Ukai, T. Yang and H.-J. Zhao: Optimal decay
estimates on the linearized Boltzmann equation with time-dependent forces and
their applications, Communications in
Mathematical Physics 277 (2008), no. 1, 189-236. pdf file
9.
With H.-X. Liu, S. Ukai and T. Yang: Optimal
$L^p$-$L^q$ Convergence rates for the Navier-Stokes equations with potential
force, Journal of Differential Equations
238 (2007), no. 1, 220-233. pdf
file
10. With S. Ukai, T.
Yang and H.-J. Zhao: Optimal convergence rates for the compressible
Navier-Stokes equations with potential forces, Mathematical
Models and Methods in Applied Sciences 17 (2007), No. 5, 737-758. pdf file
11. With S.-P. Lin
and C.J. Zhu: Optimal $L^p (1\leq p\leq \infty)$ rates of decay to linear
diffusion waves for nonlinear evolution equations with ellipticity and
dissipation, Nonlinear Analysis: Theory,
Methods & Applications 66 (2007), no. 11, 2335-2344. pdf file
12. With T. Yang and
C.-J. Zhu: Navier-Stokes equations with degenerate viscosity, vacuum and
gravitational force, Mathematical Methods
in the Applied Sciences 30 (2007), no. 3, 347-374. pdf file
13. With T. Yang and
C.-J. Zhu: Existence of stationary solutions to the Vlasov-Poisson-Boltzmann
system, Journal of Mathematical Analysis
and Applications 327 (2007), no. 1, 425-434. pdf file
14. With S.-Q. Tang
and C.-J. Zhu: Asymptotics in nonlinear evolution system with dissipation and
ellipticity on quadrant, Journal of
Mathematical Analysis and Applications 323 (2006), no. 2, 1152-1170. pdf file
15. With M. Zhang
and C.-J. Zhu: $L^1$ stability for the Vlasov-Poisson-Boltzmann system around
vacuum, Mathematical Models and Methods
in Applied Sciences 16 (2006), No. 9, 1505-1526. pdf file
16. With T. Yang and
C.-J. Zhu: $L^1$ and BV-type stability of the Botlzmann equation with external
forces, Journal of Differential Equations
227 (2006), no. 1, 1-28. pdf file
17. With T. Yang and
C.-J. Zhu: Boltzmann equation with external force and Vlasov-Poisson-Boltzmann
system in infinite vacuum, Discrete and
Continuous Dynamical Systems 16 (2006), no. 1, 253-277. pdf file
18. With T. Yang and
C.-J. Zhu: Global existence to Boltzmann equation with external force in
infinite vacuum, Journal of Mathematical
Physics 46 (2005), 053307, 13pp. pdf file
19. With C.-J. Zhu:
Asymptotics of dissipative nonlinear evolution equations with ellipticity:
different end states, Journal of
Mathematical Analysis and Applications 303 (2005), no. 1, 15-35.
20. With C.-J. Zhu:
A note on semiconcave function, Applicable
Analysis 82 (2003), no. 9, 889-894.
21. With C.-J. Zhu:
Existence and uniqueness of entropy solution to initial boundary value problem
for the inviscid Burgers equation, Journal
of Physics. A. 36 (2003), no. 8, 2099-2107.
Conference Papers and Short
Surveys
1.
With S. Ukai and T. Yang: A combination of energy
method and spectral analysis for studies on systems for gas motions, Frontiers of Mathematics in China 4
(2009), no. 2, 253-282. pdf
file
2.
The Boltzmann equation near equilibrium states in
${\bf R}^n$, Methods and Applications of
Analysis 14 (2007), No. 3, 227-250. pdf file
Submitted Papers
1.
With A. Lorz and P. Markowich: Global Solutions to
the coupled chemotaxis-fluid equations, submitted preprint (May 4, 2009). pdf file
2.
With M. Fornasier and G. Toscani: A kinetic
flocking model with diffusions, submitted preprint (Sep. 10, 2009). pdf
file
3.
Hypocoercivity of linear degenerately dissipative kinetic
equations, submitted preprint (Dec. 3, 2009). pdf file
Work in Progress
1.
Large-time behavior of the Vlasov-Maxwell-Boltzmann
system.
Note: Some information in
this part can change as time goes on.
PhD
Thesis
Title:
Some Mathematical Theories on the Gas
Motion Under the Influence of External Forcing pdf
file
Note: Most of the
information in the thesis has been published in the form of research papers.
Last updated on January 23, 2010 by Renjun
Duan
