Your browser do not support script. Here are news slide. Research Staff

Liu, Tai-Ping

photo

Dr. Liu's research interests center around Nonlinear partial differential equations, shock wave theory, and kinetic theory.

 


Email : tpliu AT math.sinica.edu.tw
Phone:+886 2 2368-5999 ext. 704
Fax: +886 2 2368-9771

Publications :

1.  The Riemann problem for general 2 X 2 conservation Laws, Transactions of A.M.S. , 199(1974), 89-112
2.  The Riemann Problem for general systems of conservation laws, J. Diff. Equations , 18(1975), 218-234
3.  Existence and uniqueness theorems for Riemann problems, Transactions of A.M.S. , 212(1975), 375-382
4.  Uniqueness theorem of the Cauchy problem for general 2 X 2 conservation laws, J. Diff. Eqs. , 20(1976), 369-388
5.  Shock waves in nonisentropic gas flow, J. Diff. Equations , 22(1976), 442-452
6.  The entropy condition and the admissibility of shocks, J. of Math. Anal. and Applications , 53(1976), 75-88
7.  Solutions in the large for equations of nonisentropic gas dynamics, Indiana Univ. J. , 26(1977), 144-177
8.  Initial-boundary value problems for gas dynamics, Arc. Rat. Mech. and Anal. , 64(1977), 137-168
9.  Decay to N-waves of solutions of general systems of nonlinear hyperbolic conservation laws, Comm. Pure Appl. Math , 30(1977), 586-611
10.  Large-time behavior of solutions of initial and initial-boundary value problem of general system of hyperbolic conservation laws, Comm. Math. Phys. , 55(1977), 163-177
11.  Linear and nonlinear large-time behaviors of solutions of hyperbolic conservation laws, Comm. Pure Appl. Math. , 30(1977), 767-796
12.  The deterministic version of the Glimm scheme, Comm. Math. Phys. , 57(1977), 135-148
13.  Asymptotic behavior of solutions of general systems of nonlinear hyperbolic conservation laws, Indiana Univ. J. , 27(1978), 211-253
14.  Invariants and asymptotic behavior of solution of a conservation law, Proceedings of A.M.S. , 71(1978), 227-231
15.  The free piston problem for gas dynamics, J. of Diff. Equations , 39(1978), 175-191
16.  (with S. Antman) Traveling waves in hyperelastic rods, Quarterly of Appl. Math. , 36(1979), 377-399
17.  Development of singularities in the nonlinear waves for quasilinear hyperbolic partial differential equations, J. Diff. Equations, , 33(1979), 92-111
18.  Quasilinear hyperbolic systems68, Comm. Math. Phys. , 68(1979), 142-172
19.  A system of quasilinear hyperbolic partial differential equations. Trends in applications of pure mathematics to mechanics, Vol. III (Edinburgh, 1979), 179-189., (1979)
20.  probleme du vide pour les equations de la dynamique des gaz isentropiques. (French) [The problem of the vacuum for equations in isentropic gas dynamics] Nonlinear partial differential equations and their applications. Collège de France Seminar, Vol. II (Paris, 1979/1980), 319--326, 395., (1979/1980)
21.  (with J. Smoller) On the vacuum state for isentropic gas dynamics equations, Advances in Math. , 1(1980), 345-359
22.  (with Conlon, Joseph G.) Admissibility criteria for hyperbolic conservation laws, Indiana Univ. Math. J. , 30(1981), no. 5, 641-652
23.  Admissible solutions of hyperbolic conservation laws, Memoirs, Amer. Math. Soc. , 240(1981)
24.  Transonic gas flow in a duct of varying area, Arch. Rat. Mech. and Anal. , 80(1982), 1-18
25.  Nonlinear stability and instability of transonic flows through a nozzle, Comm. Math. Phys. , 83(1982), 243-260
26.  (with A. Chorin and Z. H. Teng) Riemann problems for reacting gas with applications to transitions, SIAM J. Appl. Math. , 42(1982), 964-981
27.  Resonance for quasilinear hyperbolic equation, Bulletin Amer. Math. Soc. , 6(1982), 463-465
28.  (with C. Li) Asymptotic states for hyperbolic conservation laws with a moving source, Advances in Appl. Math. , 4(1983), 353-379
29.  (with M. Pierre) Source-solutions and asymptotic behavior in conservation law, J. Diff. Equ. , 51(1984), 419-441
30.  (with H. Galz) The asymptotic analysis of wave interactions and numerical calculations of transonic nozzle flow, Advances Appl. , 5(1984), 111-146
31.  Stability of nonlinear waves. Metastability and incompletely posed problems, Minneapolis, Minn. (1985), 259-267
32.  (with C. H. Wang) On a system of nonstrictly hyperbolic system, J.D.E. , 57(1985), 1-14
33.  Nonlinear stability of shock waves for viscous conservation laws, Amer. Math. Soc. (N.S.) , 12(1985), no. 2, 233-236
34.  Nonlinear stability of shock waves for viscous conservation laws, Memoirs, Amer. Math. Soc. , 328(1985)
35.  Shock waves and diffusion waves. Nonlinear systems of partial differential equations in applied mathematics, Part 1 (Santa Fe, N.M., 1984), 283--291, Lectures in Appl. Math., 23, Amer. Math. Soc., Providence, RI, 1986., (1986)
36.  (with L. P. Huang) Piecewise steady elements and Godunov-type difference scheme for duct flow, Comp. & Maths. with Appls. , 12A(1986), 377-388
37.  Shock waves for compressible Navier-Stokes equations are stable, Comm. Pure Appl. Math. , 39(1986), 565-594
38.  (with R. Caflisch) Stability of shock waves for the Broadwell equations, Comm. Math. Phys. , 39(1986), 565-594
39.  (with I-L. Chern) Convergence to diffusion waves of solutions for viscous conservation laws, Comm. Math. Phys. , 110(1987), 503-517
40.  Hyperbolic conservation laws and related topics. Partial differential equations of hyperbolic type and applications, 113--139, World Sci. Publishing, Singapore, 1987., (1987)
41.  Pointwise convergence to math symbols by mimetex-waves for hyperbolic conservation laws, Bulletin, Inst. Math., Academia Sinica , 15(1987), 1-17
42.  Hyperbolic conservation laws with relaxation, Comm. Math. Phys. , 108(1987), 153-175
43.  Nonlinear resonance for quasilinear hyperbolic equation, J. Math. Phys. , 28(1987), 2593-2602
44.  Nonlinear waves for viscoelasticity with fading memory, J. Diff. Equ. , 76(1988), 26-46
45.  (with Z. Xin) Nonlinear stability of rarefaction waves for compressible Navier--Stokes equations, Comm. Math. Phys. (1988), 451-465
46.  Quasilinear hyperbolic-parabolic partial differential equations, Algebra, analysis and geometry (Taipei) (1988), 185-197
47.  (with Hsu, Sze-Bi) Local uniqueness of interior layer solution and its related stability property., Nonlinear analysis (Taipei) (1989), 51-60
48.  (with D. Hoff) The inviscid limit for the Navier-Stokes equations of compressible, instropic flow with shock data, Indiana Univ. J. , 38(1989), 861-915
49.  Geometric theory of shock waves. Multidimensional hyperbolic problems and computations (Minneapolis, MN, 1989), 198-202., (1989)
50.  Nonlinear analysis. Papers from the conference held in Taipei, June 19--24, 1989, (1989)
51.  Nonlinear hyperbolic waves. Nonlinear hyperbolic equations in applied sciences. Rend. Sem. Mat. Univ. Politec. Torino 1988, Special Issue, 269--277 (1989)., (1989)
52.  (with Z. Xin) Over compressive shock waves nonlinear evolution equations that change types, ed. B. Keyfitz and M. Shearer, IMA volumes in Math Appls. , 27(1990), 139-145
53.  (with S. Hsu) Nonlinear singular Sturm-Liouville problem and application to transonic flow through a nozzle, Comm. Pure Appl. Math. , 43(1990), 31-61
54.  On the viscosity criterion for hyperbolic conservation laws. Viscous profiles and numerical methods for shock waves (Raleigh, NC, 1990), 105-114., (1990)
55.  (with T. Zheng) A scalar combustion model, Arch. Rational Mech. Anal. , 114(1991), 297-312
56.  Viscosity criterion for hyperbolic conservation laws, Proc. SIAM. Ed. M. Shearer (1991)
57.  Nonlinear hyperbolic-parabolic p.d.e., Nonlinear Analysis, Academia Sinica, R.O.C., World Scientific (1991), 161-170
58.  Interaction of nonlinear hyperbolic waves, Nonlinear Analysis, Academia Sinica, R.O.C., World Scientific (1991), 171-184
59.  (with Z. Xin) Stability of viscous shock waves associated with a nonstrictly hyperbolic conservantion law, Comm. Pure Appl. Math., XLV (1992), 361-388., (1992)
60.  (with S. Cox) Zero-memory limit for a viscoelasticity model with Riemann data (preprint).,
61.  (with L. Hsiao) (with ) Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping, Comm. Math. Phys. , 143(1992), 599-605
62.  (with G.-Q. Chen) Zero relaxation and dissipation limits for hyperbolic conservation laws, Comm. Pure Appl. Math. , 46(1993), 755-781
63.  (with H. Freistühler) Nonlinear stability of overcompressive shock waves in a rotationally invariant system of viscious conservation laws, Comm. Math. Physics , 153(1993), 147-158
64.  (with P. Le Floch) Existence theory for nonlinear hyperbolic systems in nonconservative form, Forum Math. , 5(1993), 261-280
65.  (with L. Hsiao) Nonlinear diffusive phenomena of nonlinear hyperbolic systems, Chin.Ann. Math. , 14B(1993), 465-480
66.  Nonlinear evolutionary partial differential equations., Proceedings of the International Conference held in Beijing (1993-06), 21-25
67.  Nonlinear waves for viscous conservation laws, Nonlinear evolutionary partial differential equations (1993), 65-74
68.  (with Hsiao, Ling) Nonlinear diffusive phenomena of nonlinear hyperbolic systems. A Chinese summary appears in Chinese Ann. Math. Ser. A 14 (1993), no. 6, 740. Chinese Ann. Math. Ser. B 14 (1993), no. 4, 465--480., (1993)
69.  (with Bolliat, G.) Dafermos, C. M.; Lax, P. D. Recent mathematical methods in nonlinear wave propagation. Lectures given at the 1st C.I.M.E. Session held in Montecatini Terme, May 23--31, 1994., (1994-05)
70.  (with G.-Q. Chen and D. Levermore) Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Applied Math. , 47(1994), 787-830
71.  (with L. Ying) Nonliner stability strong detonations for a combustion model, SIAM J. of Math. Anal. , 26(1995), 519-528
72.  (with K. Zumbrun) Nonlinear stability of an undercompressive shock for complex Burgers equation, Comm. Math. Physics , 168(1995), 163-186
73.  (with K. Zumbrum) On nonlinear stability of general undercompressive viscous shock waves, Comm. Math. Phys. , 175(1995), 319-345
74.  Stability and viscosity criterion of shocks. Proceedings of the VIII International Conference on Waves and Stability in Continuous Media, Part I (Palermo, 1995). Rend. Circ. Mat. Palermo (2) Suppl. No. 45, part I (1996), 357--366., (1996)
75.  Nonlinear hyperbolic-dissipative partial differential equations. Recent mathematical methods in nonlinear wave propagation (Montecatini Terme, 1994), 103--136, Lecture Notes in Math., 1640, Springer, Berlin, 1996., Recent mathematical methods in nonlinear wave propagation (1994/1996)
76.  Gas flows with damping and vacuum, Japan J. Indus. and Appl. Math. , 13(1996), 25-32
77.  (with D. Li and D. Tan) Stability of strong detonation travelling waves to combustion model, J. Math. Anal. Appl. , 201(1996), 516-531
78.  (with Y. Zeng) Large time behavior of solutions of general quasilinear hyperbolic-parabolic systems of conservation laws, Memoirs, Amer. Math. Soc. , 599(1997)
79.  (with S. Yu) Propagation of Burgers stationary shocks under boundary effect, Archive Rational Mech. Anal. , 139(1997), 57-82
80.  Pointwise convergence to shock waves for viscous conservaton laws, Comm. Pure Appl. Math. L (1997), Comm. Pure Appl. Math. , L(1997), 1113-1182
81.  (with T. Yang) Compressible Euler equations with vacuum, J.D.E. , 140(1997), 223-237
82.  (with Z. Xin) Pointwise decay to contact continuities for viscous conservation laws, Asian J. Math. , 1(1997), 34-84
83.  (with K. Nishihara) Asymptotic behaviour for scalar viscous conservation law with boundary effect, J.D.E. , 133(1997), 296-320
84.  (with T. Yang) L1 stability of constant states for hyperbolic conservation laws, Methods and Appl. Analysis , 4(1997), 339-355
85.  Regularization of solution operators for quasilinear hyperbolic-parabolic partial differential equations, J. Partial Differential Equations , 10(1997), no. 4, 347-354
86.  (with Y. Zeng) Compressible Navier-Stokes equations with zero heat conductivity, J. D. E. (1998)
87.  (with S.-H. Yu) Continuum shock profiles for discrete conservation laws, I. Construction, Comm. Pure Appl. Math. (1998)
88.  (with W. Wang) The pointwise estimates of diffusion wave for the Navier-Stokes systems in odd dimensions, Comm. Math. Phys. , 196(1998), 145-173
89.  (with W.-C. Lien) Nonlinear stability of a self-similar 3-dimensional gas flow, Comm. Math. Phys. , 204(1999), no. 3, 525-549
90.  Zero dissipation and stability of shock waves, Methods and Appl. Analysis , 5(1998), 81-94
91.  (with Z. Xin and T. Yang) Vacuum states for compressible flow, Disc. Cont. Dyn. Ana. , 4(1998), 1-32
92.  (with T. Yang) (with ) L1 stability of 2x2 systems of hyperbolic conservation laws, J. Amer. Math. Soc. (1998), 729-772
93.  (with T. Yang) L1 stability of conservation laws with coinciding Hugoniot and characteristic curves, Indiana Univ. Math. J. (1998)
94.  (with SIAM J. Math. Anal.) Behaviours of solutions for the Burgers equation with boundary corresponding to rarefaction waves, A. Matsumura and K. Nishihar , 29(1998), 293-308
95.  (with A. Bressan and T. Yang) L1 stability estimates for nxn conservatiob laws, Archive Rational Mech. Anal. (1998)
96.  (with T. Yang) A generalized entropy for scalar conservation laws, Comm. Pure Appl. Math. , LII(1999), 1427-1442
97.  (with S.-H. Yu) Continuum shock profiles for discrete conservation laws, II. Stability. Comm. Pure Appl. Math. LII (1999), 1047-1073., (1999)
98.  (with T. Yang) Well-posedness theory for hyperbolic conservation l aws, Comm. Pure Appl. Math. LII, Comm. Pure Appl. Math. , II(1999), 1553-1586
99.  (with S.-H. Yu) Nonlinear stability of weak detonation waves for a combustion model, Comm. Math. Phys. , 204(1999), 551-586
100.  (with W.-C. Lien) Nonlinear stability of a self-similar 3-dimensional gas flow, Comm. Math. Phys. , 204(1999), no. 3, 525-549
101.  (with Yang, Tong) Well-posedness theory for system of hyperbolic conservation laws. Hyperbolic problems: theory, numerics, applications, Vol.II, (Z�rich,1998), 681-691, Internat. Ser. Numer. Math., 130, Birkh酳ser, Basel, 1999., , II(1998/1999)
102.  L1 stability for systems of hyperbolic conservation laws.'' Nonlinear partial differential equations (Evanston, IL, 1998), 183-192, Contemp. Math., 238, Amer. Math. Soc., Providence, RI, 1999., Yang, Tong (1999)
103.  (with S.H. Yu) 145Hyperbolic conservation laws and dynamic systems, Discrete Contin. Dynam. Systems , 6(2000), no. 1, 143-145
104.  Hyperbolic and Viscous Conservation Laws. CBMS-NSF Regional Conference Series in Applied Mathematics, 72. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2000., (2000)
105.  Shock waves. Proceedings of the International Congress of Mathematicians, Higher Ed. Press (Beijing) , III(2002), 185-188
106.  (with T. Yang and Y. Zheng) Some nonlinear functionals for scalar conservation laws, Methods Appl. Anal. , 8(2001), no. 4, 609-622
107.  (with T. Yang) Weak Solutions to General Systems of Hyperbolic Conservation Laws, Comm. Math. Phys. , 230(2002), no. 2, 289-327
108.  (with T. Ruggeri) Entropy production and admissibility of shocks, Acta Math. Appl. Sin. Engl. Ser. , 19(2003), 1-12
109.  (with Y. Deng, T. Yang, and T. Yao) Solutions with vacuum for Euler-Poisson equations, Arch. Rational Mech. Anal. , 164(2002), no. 3, 261-285
110.  (with Yu, Shih-Hsien) Boltzmann equation: micro-macro decompositions and positivity of shock profiles, Comm. Math. Phys. , 246(2004), no. 1, 133-179
111.  (with Yang, Tong; Yu, Shih-Hsien) Energy method for Boltzmann equation, Phys. D , 188(2004), no. 3-4, 178-192
112.  (with Yu, Shih-Hsien) (with ) The Green's function and large-time behavior of solutions for one-dimensional Boltzmann equation, Comm. Pure. Appl. Math. , 57(2004), no. 12, 1543-1608
113.  (with C.-C. Chen and T. Yang) Existence of boundary layer solutions to the Boltzmann equation, Anal. Appl. (Singap.) , 2(2004), no. 4, 337-363
114.  (with C.-Y., Lan;H.-E., Lin;S.-H. Yu) Propagation of viscous shock waves away from the boundary., SIAM J. Math. Anal. , 36(2004), no. 2, 580-617
115.  (with V. Elling) The ellipticity principle for self-similar potential flows., J. Hyperbolic Differ. Equ. , 2(2005), no. 4, 909-917
116.  (with T. Yang, S.-H. Yu, H.-J. Zhao) Nonlinear stability of rarefaction waves for the Boltzmann equation., Arch. Rational Mech. Anal. , 181(2006), no. 2, 333-371
117.  (with S.-H. Yu) Green's function of Boltzmann equation, 3-D, Bull. Inst. Math. Acad. Sin. (N.S.) , 1(2006), no. 1, 1-78
118.  (with Chen, Chiun-Chuan; Chen, I-Kun; Sone, Yoshio) Thermal transpiration for the linearized Boltzmann equation., Comm. Pure Appl. Math. , 60(2007), no. 2, 147-163
119.  (with Lee, Ming-Yi; Yu, Shih-Hsien) Large-time behavior of solutions for the Boltzmann equation with hard potentials., Comm. Math. Phys. , 269(2007), no. 1, 17-37
120.  (with Yu, Shih-Hsien) Initial-boundary value problem for one-dimensional wave solutions of the Boltzmann equation., Comm. Pure Appl. Math. , 60(2007), no. 3, 295-356
121.  (with Elling, Volker) Supersonic flow onto a solid wedge., Comm. Pure Appl. Math. , 61(2008), no. 10, 1347-1448
122.  (with Yu, Shih-Hsien) Diffusion under gravitational and boundary effects., Bull. Inst. Math. Acad. Sin. (N.S.) , 3(2008), no. 1, 167-210
123.  (with S.-H., Yu) Boltzmann equation, boundary effects., Discrete Contin. Dyn. Syst. , 24(2009), no. 1, 145-157
124.  (with Y., Zeng) Time-asymptotic behavior of wave propagation around a viscous shock profile., Comm. Math. Phys. , 290(2009), no. 1, 23-82
125.  (with S.-H., Yu) Viscous shock wave tracing, local conservation laws, and pointwise estimates, Bull. Inst. Math. Aca. (N.S.) , 4(2009), no. 3, 167-210
126.  (with Zeng, Yanni) On Green's function for hyperbolic-parabolic systems, Acta Math. Sci. Ser. B Engl. Ed. , 29(2009), no. 6, 1556-1572
127.  (with Kuo, Hung-Wen; Noh, Se Eun) Mixture lemma, Bull. Inst. Math., Acad. Sin. (N.S.) , 5(2010), no. 1, 1-10
128.  (with Yu S.-H.) Viscous rarefaction waves, Bull. Inst. Math. Acad. Sin. (N.S.) , 5(2010), no. 2, 123-179
129.  (with S.-H. Yu; Y. Zeng) Viscous Conservation Laws, Part I: Scalar Laws, Bull. Inst. Math., Acad. Sin. (N.S.) , 5(2010), no. 3, 233-310
130.  (with Yu, Shih-Hsien) Solving Boltzmann equation, Part I: Green's function, Bull. Inst. Math. Acad. Sin. (N.S.) , 6(2011), no. 1, 115-243
131.  (with Yu S.-H.) On boundary relation for some dissipative systems, Bull. Inst. Math. Acad. Sin. (N.S.) , 6(2011), no. 3, 245-267
132.  Multi-dimensional gas flow: some historical perspectives, Bull. Inst. Math. Acad. Sin. (N.S.) , 6(2011), no. 3, 269-291
133.  (with Yu S.-H.) Dirichlet-Neumann kernel for hyperbolic-dissipative system in half-space, Bull. Inst. Math. Acad. Sin. (N.S.) , 7(2012), no. 4, 477-543
134.  (with Kuo, Hung-Wen and Tsai, Li-Cheng) Free molecular flow with boundary effect, Comm. Math. Phys. , 318(2013), no. 2, 375-409
135.  Aspects of dissipation for compressible fluids and kinetic theory, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. , 371(2013), no. 2005
136.  (with Yu, Shih-Hsien) Invariant manifolds for steady Boltzmann equation and applications, Archive Rational Mechanics and Analysis , 209(2013), no. 3, 869-997
137.  (with Chen, I-Kun and Takata, Shigeru) Boundary singularity for thermal transpiration problem of the linearized Boltzmann equation, Arch. Ration. Mech. ANal. , 212(2014), no. 2, 575-595
138.  Equilibrating effects of boundary and collision in rarefied gases., Comm. Math. Phys. , 318(2014), no. 2, 421-480
139.  (with Yu, Shih-Hsien) Fujita equation with boundary effect, Bull. Inst. Math. Acad. Sin. (N.S.) , 9(2014), no. 2, 267-282
140.  (with Yu, Shih-Hsien) Boundary wave propagator for compressible Navier-Stokes equations., Found. Comput. Math. , 14(2014), no. 6, 1287-1335
141.  (with Zeng, Yanni) Shock waves in conservation laws with physical viscosity., Mem. Amer. Math. Soc. , 234(2015), no. 1105
142.  (with Noh, Se Eun) Wave propagation for the compressible Navier-Stokes equations., J. Hyperbolic Differ. Equ. , 12(2015), no. 2, 385-445
143.  (with Chen, I-Kun; Funagane, Hitoxhi; and Takata, Shigeru) Singularity of the velocity distribution function in molecular velocity space., Comm. Math. Phys. , 341(2016), no. 1, 105-134
144.  Hopf-Cole transformation, Bull. Inst. Math. Acad. Sin. (N.S.) , 12(2017), no. 1, 71-101