Name: Tai-Chia Lin

Address: Department of Mathematics,

National Taiwan University,

No. 1, Sec. 4, Roosevelt Road, Taipei, 10617 Taiwan

**EDUCATION AND EMPLOYMENT**

l Professor, 2004 --, Department of
Mathematics, National Taiwan University.

l Associate Professor, 2000 -- 2004,
Department of Mathematics, National
Chung Cheng University.

l Assistant Professor, 1997 -- 2000,
Department of Mathematics, National Chung Cheng University.

l Posdoctor, 1996 -- 1997, Mathematical
Sciences of Research Institute (MSRI), UC-Berkeley.

l Ph.D. Mathematics, May 1996, Courant
Institute of Mathematical Sciences, New York University.

l M.S. Applied Mathematics, June 1989,
National Tsing Hua University.

l B.S. Applied Mathematics, June 1987,
National Chiao-Tung University.

EXPERIENCE

l Associate editor of Taiwanese Journal of
Mathematics 2014-2017

l Chief editor of Taiwanese Journal of
Mathematics 2017-2018

l Visiting professor at Illinois Institute of
Technology, August 10th to September 9th

l (2017).

l Shapiro visiting professor at Penn State
University, August 2^{nd} to September 9^{th}, 2012, July 8^{th}
to August 22^{nd} , 2013, July 20^{th} to August 19^{th},
2014..

l Researcher of TAMU (Texas A&M
University) at Qatar, February 10^{th} to April 10^{th}, 2012,
January 13^{th} to February 17^{th}, 2013, January 23^{rd}
to February 15^{th}, 2014.

l Researcher of IMA (Institute of Mathematics
and its Application, University of Minnesota, USA), 8/1/2008-7/31/2009,
12/7-11/2009, 4/8-16/2010

l Invited short term visits: Ohio State Univ.
(December 2-5, 2008), New York Univ. (December 16-31, 2008), Penn State Univ.
(February 17-24, 2009), Univ. of Tennessee (April 6-9, 2009), Purdue Univ.
(April 28-May 1, 2009), Univ. of Kentucky (May 10-13, 2009), The Chinese Univ.
of Hong Kong (9/1-8/2006, 10/2-7/2007, 6/6-15/2008, 4/2-7/2010, 1/4-8/2011,
4/23-27/2012)

l Mainland China (Hangzhou, Shanghai
6/3-11/2011, 6/15-19/2014, Hangzhou, Kaifeng 6/12-22/2013)

**Invited Speaker:
**

1.
2017 International
Workshop on “Fundamental Problems in Mathematical and

Theoretical Physics” (July 24-28, Waseda
University, Tokyo, Japan) 3 times

lectures (90 min x 3), Title: Analysis of
Nonlinear Schrȍdinger equations and its

applications

2.
Workshop
on Mathematical Approaches to Interfacial Dynamics in Complex

Fluids, Banff International Research Station,
June 26-30, 2017

3.
SIAM 2017
East Asian Section Conference, Seoul National University, June

22-25, 2017

4.
MSJ
Autumn Meeting 2016, Kansai University, Japan, September 15, 2016

5.
BIRS
Workshop: Ion Transport, Electrodiffusion, Electrohydrodynamics and

Homogenization, May 29-June 3, 2016, Banff
International Research Station,

Canada.

6.
MBI
Workshop on Modeling and Computation of Transmembrane Transport,

November 16-20, 2015, Mathematical Biosciences
Institute, Ohio State

University, USA.

7.
IMA
Workshop "Mathematics of Biological Charge Transport: Molecules and
Beyond", July 19-25, 2015, University of Minnesota, USA

8.
Interdisciplinary
Mathematics toward Smart Innovations, Tohoku University, Japan, March 26-28,
2015

9.
2014 SIAM
Conference of the Life Sciences, August 4-7, 2014, Charlotte, North Carolina,
USA

10.
Workshop
on transport of ionic particles in biological environments, Fields Institute,
Toronto, Canada, July 28-August 1, 2014

11.
FACM
meeting, NJIT, USA, May 18-20, 2012

12.
SIAM
Conference on Analysis of Partial Differential Equations, San Diego, California
USA, November 14-17, 2011

13.
Recent
Development in Nonlinear Partial Differential Equation, The Croucher Foundation
Advanced Study Institute, CUHK, February 28-March 4, 2011

**Referee
of Journals:
**

l SIAM J Math Analysis (2012, 2015-)

l SIAM J Applied Math (2016-)

l Journal of Differential Equations (2005,
2011, 2012-)

l Calculus of Variations and PDE (2008,
2012-)

l Journal of Functional Analysis (2015-)

l Nonlinearity (2008, 2013-)

l Indiana University Mathematics Journal
(2009)

l Journal of Computational Physics (2009)

l Communications in Mathematical Sciences
(2009, 2013-)

l Discrete and Continuous Dynamical Systems
(2010, 2013-)

l Physica D (2016-)

**Fields of specialty**** **partial differential equations,
mathematical physics

**HONORS**

l Academic Award
of Ministry of Education, 2022 (65 屆教育部學術獎)

l TWSIAM Fellow,
2020, Taiwan Society for Industrial and Applied Mathematics (台灣工業與應用數學會會士)

l NTU Core
Consortiums（台大核心群計畫）, 2018-2020

l Academic
Award, 2016, Mathematical Society of ROC (TMS)

l Outstanding
Research Award, 2015, Ministry of Science and Technology (MOST) (科技部傑出獎)

l Thematic
Program MOST（科技部主軸計畫）, 2013-2017

l Young
Mathematician Award, Mathematical Society of ROC (TMS), 2005.

l Outstanding
Research Award, 2003, National Science Council (國科會傑出獎)

**Publication:**

1.
J.H. Lyu, C.C. Lee and T.C.
Lin, Near- and far-field expansions for stationary solutions of
Poisson-Nernst-Planck equations, Math Meth Appl Sci. (2021) 1–24.

2.
Q. Hou, T.C. Lin and Z.A.
Wang, On a singularly perturbed semi-linear problem with Robin boundary
conditions, DCDS-B, Volume 26, Number 1 (2021) 401-414.

3.
C.Y. Hsieh, T.C. Lin, C. Liu
and P. Liu, Global existence of the non-isothermal
Poisson-Nernst-Planck-Fourier system, Journal of Differential Equations
269(2020) 7287-7301.

4.
4. T.C. Lin and T.F. Wu, Multiple
positive solutions of saturable nonlinear Schrodinger equations with intensity
functions, Discrete and Continuous Dynamical Systems A, Volume 40, Number 4
(2020) 2165-2187.

5.
Q. Gao, C.C. Lee and T.C. Lin,
Semi-classical analysis with new Galilean transformations for a
Gross-Pitaevskii system with non-zero conditions at infinity, Z. Angew.
Math.Phys.(2019) 70:78 (1-25).

6.
T.C. Lin, M.R. Belic, M.S.
Petrovic, H. Hajaiej and G. Chen, The virial theorem and ground state energy
estimate of nonlinear Schrȍdinger equations in R2 with square root and
saturable nonlinearities in nonlinear optics, Calculus of Variations and
Partial Differential Equations, Vol.56, No.5 (2017) 147 (1-20).

7.
T.C. Lin, X. Wang and Z.Q.
Wang, Orbital stability and energy estimate of ground states of saturable
nonlinear Schrȍdinger equations with intensity functions in R2, Journal of
Differential Equations, Vol.263, No.8 (2017), pp.2750-2786.

8.
T.L. Horng, P.H. Tsai, and
T.C. Lin, Modification of Bikerman model with specific ion sizes, Mol. Based
Math. Biol. 2017; 5:142–149.

9.
C. C. Lee, H. Lee, Y. Hyon, T.
C. Lin and C. Liu, Boundary layer solutions of charge conserving
Poisson-Boltzmann equations: one dimensional case, Comm. Math. Sci. Vol. 14,
No.4(2016), 911-940.

10.
C.Y. Hsieh and T.C. Lin, Exponential
decay estimates for the stability of boundary layer solutions to
Poisson-Nernst-Planck systems: one spatial dimension case, SIAM J. Math. Anal.
Vol.47, No.5(2015), pp. 3442–3465.

11.
T. C. Lin and B. Eisenberg,
Multiple solutions of steady-state Poisson-Nernst-Planck equations with steric
effects, Nonlinearity 28 (2015) 2053–2080.

12.
H. Wu, T.C. Lin and C. Liu,
Diffusion limit of kinetic equations for multiple species charged particles,
Arch. Rational Mech. Anal. 215 (2015) 419–441.

13.
C. Y. Hsieh, Y. Hyon, H. Lee,
T. C. Lin and C. Liu, Transport of Charged Particles: Entropy Production and
Maximum Dissipation Principle, J. Math. Anal. Appl., 422 (2015) 309-336.

14.
T.C. Lin, Milivoj R. Beli´c,
Milan S. Petrovi´c and Goong Chen, Ground states of nonlinear Schrȍdinger
systems with saturable nonlinearity in R2 for two counterpropagating beams,
Journal of Mathematical Physics, 55, 011505(1-13), 2014.

15.
T.C. Lin and Z.A. Wang,
Development of traveling waves to an interacting two-species chemotaxis model,
Discrete and Continuous Dynamical Systems A, Volume 34, Number 7 (2014)
2907-2927.

16.
T.C. Lin and B. Eisenberg, A
new approach to the Lennard-Jones potential and a new model: PNP-steric
equations, Communications in Mathematical Sciences, Vol. 12, No. 1 (2014)
149–173.

17.
H. Berestycki, T.C. Lin, J.
Wei, C. Zhao, On Phase-Separation Model: Asymptotics and Qualitative
Properties, Archive for Rational Mechanics and Analysis, 208 (2013) 163–200.

18.
T. C. Lin, Milivoj R. BeliÅLc,
Milan S. PetroviÅLc, Najdan B. AleksiÅLc and Goong Chen, Ground-state
counterpropagating solitons in photorefractive media with saturable
nonlinearity, J. Opt. Soc. Am. B / Vol. 30, No. 4 / (2013) 1036-1040.

19.
A.M. Kamchatnov, Y.H. Kuo,
T.C. Lin, T.L. Horng, S.C. Gou, R. Clift, G.A. El, R.H.J. Grimshaw, Transcritical
flow of a stratified fluid over topography: analysis of the forced Gardner
equation, J. Fluid Mech. (2013), vol. 736, pp.495-531.

20.
B. Eisenberg, T.L. Horng, T.C.
Lin and C. Liu, Steric PNP (Poisson-Nernst-Planck): Ions in Channels,
Biophysical Journal, 2013, 104:509a.

21.
T.C. Lin and T.F. Wu,
Existence and multiplicity of positive solutions for two coupled nonlinear
Schr.dinger equations, Discrete and Continuous Dynamical Systems A, Volume 33,
No. 1, 2013, 2911-2938.

22.
T.C. Lin, J. Wei and J. Yang,
Vortex rings for the Gross-Pitaevskii equation zz0905 in R3, J. Math. Pures
Appl. 100 (2013) 69–112.

23.
A. M. Kamchatnov, Y.H. Kuo,
T.C. Lin, T.L. Horng, S.C. Gou, R. Clift,G. A. El, R. H. J. Grimshaw, Undular
bore theory for the Gardner equation, Phys. Rev. E, 86, 036605 (2012).

24.
T.L. Horng, T.C. Lin, C. Liu
and B. Eisenberg, PNP equations with Steric Effects: a Model of Ion Flow
through Channels, The Journal of Physical Chemistry B, 2012. 116 (37), p.
11422-11441.

25.
C.-H. Hsueh, T.-C. Lin, T.-L.
Horng, and W. C. Wu, Quantum crystals in a trapped Rydberg-dressed
Bose-Einstein condensate, Phys. Rev. A 86, 013619 (2012).

26.
C. C. Lee, H. Lee, Y. Hyon, T.
C. Lin and C. Liu, New Poisson–Boltzmann type equations: one-dimensional
solutions, Nonlinearity 24 (2011) 431–458.

27.
T. C. Lin, J. Wei and W. Yao,
Orbital stability of bound states of nonlinear Schrȍdinger equations with
linear and nonlinear optical lattices, J. Differential Equations 249 (2010)
2111–2146.

28.
X. Chen, T. C. Lin and J. Wei,
Blowup and solitary wave solutions with ring profiles of two-component
nonlinear Schr.dinger systems, Physica D 239 (2010) 613—626.

29.
F. Lin, T. C. Lin and J. Wei,
Skyrmions in Gross-Pitaevskii functional, Acta Mathematica Scientia (special
issue for Professor Wu Wenjun’s 90th birthday) 2009,29B (3), 751–776.

30.
T. L. Horng, S. C. Gou, T. C.
Lin, G. A. El, A. P. Itin, and A. M. Kamchatnov, Stationary wave patterns
generated by an impurity moving with supersonic velocity through a
Bose-Einstein condensate, Physical Review A, Vol.79, No.5, 053619(1-6) (2009).

31.
T. C. Lin, C. C. Poon and D.
H. Tsai, Expanding immersed convex plane curves, Cal. Var. P. D. E., 34 (2009),
no. 2, 153—178.

32.
C. C. Lee; T. C. Lin, Incompressible
and compressible limits of two-component Gross-Pitaevskii equations with
rotating fields and trap potentials, J. Math. Phys., 49, 043517(1-28) (2008).

33.
T. C. Lin; J. Wei, Orbital
stability of bound states of semi-classical nonlinear Schr.dinger equations
with critical nonlinearity, SIAM J. Math. Analysis, Vol 40, No. 1, (2008) pp.
365-381.

34.
T. C. Lin; J. Wei,
Half-Skyrmions and spike-vortex solutions of two-component nonlinear
Schr.dinger systems, J. Math. Phys., 48, (2007) 053518(1-21).

35.
T. L. Horng, S. C. Gou, and T.
C. Lin, Bending-wave instability of a vortex ring in a trapped Bose-Einstein
condensate, Phys. Rev. A 74, (2006) 041603(1-4)

36.
T. C. Lin, J. Wei, Symbiotic
bright solitary wave solutions of coupled nonlinear Schr.dinger equations, Nonlinearity
19, (2006) 2755-2773.

37.
T. C. Lin, J. Wei, Spikes in
two-component systems of nonlinear Schr.dinger equations with rapping
potentials, J. Diff. Eqns. 229, (2006) 538-569

38.
T. C. Lin; P. Zhang,
Incompressible and compressible limits of coupled systems of nonlinear
Schr.dinger equations. Comm. Math. Phys. 266, no. 2, (2006) 547—569

39.
T. C. Lin, J. Wei, Solitary
and self-similar solutions of two-component system of nonlinear Schr.dinger
equations. Physica D 220 (2006), no. 2, 99—115

40.
T. C. Lin, J. Wei, Ground
state of N coupled Nonlinear Schr.dinger Equations in R^n,n ≦3, Comm. Math. Phys. 255 (2005) 629-653

41.
T. C. Lin, J. Wei, Spikes in two
coupled nonlinear Schrodinger equations, Annales de L’institut Henri Poincare,
Analyse non lineaire-nonlinear analysis, 22 (2005) 403-439

42.
S. M. Chang, C.S. Lin, T.C.
Lin, W.W. Lin, Segregated nodal domains of two-dimensional multispecies
Bose-Einstein condensates, Physica D 196(2004) no.3-4, pp. 341-361.

43.
F. H. Lin, T. C. Lin, Multiple
time scale dynamics in coupled Ginzburg-Landau equations, Comm. Math. Sciences
1(2003) no.4, 671-695.

44.
T. C. Lin, L. Wang, Regularity
of the minimizer for the d-wave Ginzburg-Landau energy, Methods and
Applications of Analysis 10(2003) no.1, 81-96.

45.
F. H. Lin, T. C. Lin, Vortices
in P-wave Superconductivity, SIAM J. Math. Analy. 34(2003) 1105-1127.

46.
F. H. Lin , T. C. Lin,
Vortices in Two-Dimensional Bose-Einstein Condensates, Geom. Nonlinear PDE 29
(2002) 87-114 .

47.
S. M. Chang, T. C. Lin and W.
W. Lin, Dynamics of vortices in two-dimensional Bose-Einstein condensates, Int.
J. Bifurcation and Chaos, 12 (2002) no.4 , 739-764.

48.
Q. Han, T. C. Lin, Fourfold
symmetric vortex solutions of the d-ware Ginzburg-Landau equation,
Nonlinearity, 15 (2002) 257-269.

49.
T. C. Lin, Vortex dynamics in
d-wave superconductors, Physica D 149 (2001) 293-305.

50.
S. M. Chang, T. C. Lin and W.
W. Lin, Chaotic and quasiperiodic motions of three planar charged particles,
Int. J. Bifurcation and Chaos, 11 (2001) no. 7, 1937-1951.

51.
T. C. Lin, Instability of the
vortex solution in the complex Ginzburg-Landau equation, Nonlinear Analysis
TMA, 45 (2001), 11-17.

52.
F. H. Lin and T. C. Lin,
Vortex state of d-wave superconductors in the Ginzburg-Landau energy, SIAM J.
Math. Anal., 32 (2000) no. 3, 493-503.

53.
T. C. Lin, Rigorous and
generalized derivation of vortex line dynamics in superfluids and
superconductors, SIAM J. Appl. Math. 60 (2000) no. 3, 1099-1110.

54.
T. C. Lin, Spectrum of the
Linearized operator for the Ginzburg-Landau equation, Electron. J. Diff. Eqns.
2000 (2000) no. 42, 1-25.

55.
T. C. Lin, Vortices for the
nonlinear wave equation, Discrete and Continuous Dynamical Systems 5(1999)
no.2, 391-398.

56.
T. C. Lin, The stability of
the radial solution to the Ginzburg-Landau equation, Communication in Partial
Differential Equations, 22(3&4), 619-632(1997).

57.
F. H. Lin and T. C. Lin,
Minimax solutions of the Ginzburg-Landau equations, Selecta Mathematica, No.
3(1997) p.p. 99-113.

58.
K. S. Chang and T. C. Lin, The
structure of solutions of a semilinear elliptic equation, Trans. Amer. Math.
Soc. 332 (1992) no. 2, 535-554.