Distinguished Visiting Chair | Liu, Tai-Ping

**Contact Information**

- tpliu$\color{red}{@}$math.sinica.edu.tw
- +886 2 2368-5999 ext. 704
- +886 2 2368-9771

**Research Interests**

- Nonlinear partial differential equations
- shock wave theory
- kinetic theory

**Education**

- Ph.D. The University of Michigan (1973)
- M.S. Oregon State University (1970)
- B.S. National Taiwan University (1968)

**Links**

**Work Experience**

- Distinguished Research Fellow Institute of Mathematics, Academia Sinica, R.O.C. 2006 - Present
- Distinguished Research Fellow Institute of Mathematics,Academia Sinica, R.O.C. 2000-2005

**Awards**

- Galileo Galilei Medal , City if Padova, 2012
- Cataldo e Angiola Agostinelli International Prize, 2009
- TWAS membership, 2006
- Member, Academia Sinica, Nankang, Rep. of China, 1992
- Guggenheim Fellowship, 1982-83
- Sloan Fellowship, 1979-81
- NSF Grant, 1976-Present
- Adjunct professor, Zhejiang University, Hangzhou,
- Honorary professor, Chinese Academy of Sciences, Beijing,
- Honorary professor, City University of Hong Kong,

**Research Descriptions**

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

**Selected Publications**

- (with Jiang J.-C.) "Boltzmann collision operator for the infinite range potential: a limit problem." , 36 (6), 1639-1677, 2019.
- (with Yu S.-H.) "Multi-dimensional wave propagation over a Burgers shock profile."
,
*Archive for Rational Mechanics and Analysis*, 229 (1), 231-337, 2018. - (with Yu S.-H.) "Multi-dimensional wave propagation over a Burgers shock profile"
,
*Archive for Rational Mechanics and Analysis*, 229, 231-337, 2018. - "Hopf-Cole transformation"
,
*Bull. Inst. Math. Acad. Sin. (N.S.)*, 12 (1), 71-101, 2017. - (with Chen, I-Kun; Funagane, Hitoxhi; and Takata, Shigeru) "Singularity of the velocity distribution function in molecular velocity space."
,
*Comm. Math. Phys.*, 341 (1), 105-134, 2016. - (with Noh, Se Eun) "Wave propagation for the compressible Navier-Stokes equations."
,
*J. Hyperbolic Differ. Equ.*, 12 (2), 385-445, 2015. - (with Zeng, Yanni) "Shock waves in conservation laws with physical viscosity."
,
*Mem. Amer. Math. Soc.*, 234 (1105), 2015. - (with Yu, Shih-Hsien) "Boundary wave propagator for compressible Navier-Stokes equations."
,
*Found. Comput. Math.*, 14 (6), 1287-1335, 2014. - (with Yu, Shih-Hsien) "Fujita equation with boundary effect"
,
*Bull. Inst. Math. Acad. Sin. (N.S.)*, 9 (2), 267-282, 2014. - "Equilibrating effects of boundary and collision in rarefied gases."
,
*Comm. Math. Phys.*, 318 (2), 421-480, 2014. - (with Chen, I-Kun and Takata, Shigeru) "Boundary singularity for thermal transpiration problem of the linearized Boltzmann equation"
,
*Arch. Ration. Mech. ANal.*, 212 (2), 575-595, 2014. - "Aspects of dissipation for compressible fluids and kinetic theory"
,
*Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.*, 371 (2005), 2013. - (with Yu, Shih-Hsien) "Invariant manifolds for steady Boltzmann equation and applications"
,
*Archive Rational Mechanics and Analysis*, 209 (3), 869-997, 2013. - (with Kuo, Hung-Wen and Tsai, Li-Cheng) "Free molecular flow with boundary effect"
,
*Comm. Math. Phys.*, 318 (2), 375-409, 2013. - (with Yu S.-H.) "Dirichlet-Neumann kernel for hyperbolic-dissipative system in half-space"
,
*Bull. Inst. Math. Acad. Sin. (N.S.)*, 7 (4), 477-543, 2012. - "Multi-dimensional gas flow: some historical perspectives"
,
*Bull. Inst. Math. Acad. Sin. (N.S.)*, 6 (3), 269-291, 2011. - (with Yu S.-H.) "On boundary relation for some dissipative systems"
,
*Bull. Inst. Math. Acad. Sin. (N.S.)*, 6 (3), 245-267, 2011. - (with Yu, Shih-Hsien) "Solving Boltzmann equation, Part I: Green's function"
,
*Bull. Inst. Math. Acad. Sin. (N.S.)*, 6 (1), 115-243, 2011. - (with Yu S.-H.) "Viscous rarefaction waves"
,
*Bull. Inst. Math. Acad. Sin. (N.S.)*, 5 (2), 123-179, 2010. - (with S.-H. Yu; Y. Zeng) "Viscous Conservation Laws, Part I: Scalar Laws"
,
*Bull. Inst. Math., Acad. Sin. (N.S.)*, 5 (3), 233-310, 2010. - (with Kuo, Hung-Wen; Noh, Se Eun) "Mixture lemma"
,
*Bull. Inst. Math., Acad. Sin. (N.S.)*, 5 (1), 1-10, 2010. - (with Zeng, Yanni) "On Green's function for hyperbolic-parabolic systems"
,
*Acta Math. Sci. Ser. B Engl. Ed.*, 29 (6), 1556-1572, 2009. - (with S.-H., Yu) "Boltzmann equation, boundary effects."
,
*Discrete Contin. Dyn. Syst.*, 24 (1), 145-157, 2009. - (with S.-H., Yu) "Viscous shock wave tracing, local conservation laws, and pointwise estimates"
,
*Bull. Inst. Math. Aca. (N.S.)*, 4 (3), 167-210, 2009. - (with Y., Zeng) "Time-asymptotic behavior of wave propagation around a viscous shock profile."
,
*Comm. Math. Phys.*, 290 (1), 23-82, 2009. - (with Yu, Shih-Hsien) "Diffusion under gravitational and boundary effects."
,
*Bull. Inst. Math. Acad. Sin. (N.S.)*, 3 (1), 167-210, 2008. - (with Elling, Volker) "Supersonic flow onto a solid wedge."
,
*Comm. Pure Appl. Math.*, 61 (10), 1347-1448, 2008. - (with Yu, Shih-Hsien) "Initial-boundary value problem for one-dimensional wave solutions of the Boltzmann equation."
,
*Comm. Pure Appl. Math.*, 60 (3), 295-356, 2007. - (with Lee, Ming-Yi; Yu, Shih-Hsien) "Large-time behavior of solutions for the Boltzmann equation with hard potentials."
,
*Comm. Math. Phys.*, 269 (1), 17-37, 2007. - (with Chen, Chiun-Chuan; Chen, I-Kun; Sone, Yoshio) "Thermal transpiration for the linearized Boltzmann equation."
,
*Comm. Pure Appl. Math.*, 60 (2), 147-163, 2007. - (with S.-H. Yu) "Green's function of Boltzmann equation, 3-D"
,
*Bull. Inst. Math. Acad. Sin. (N.S.)*, 1 (1), 1-78, 2006. - (with T. Yang, S.-H. Yu, H.-J. Zhao) "Nonlinear stability of rarefaction waves for the Boltzmann equation."
,
*Arch. Rational Mech. Anal.*, 181 (2), 333-371, 2006. - (with V. Elling) "The ellipticity principle for self-similar potential flows."
,
*J. Hyperbolic Differ. Equ.*, 2 (4), 909-917, 2005. - (with C.-Y., Lan;H.-E., Lin;S.-H. Yu) "Propagation of viscous shock waves away from the boundary."
,
*SIAM J. Math. Anal.*, 36 (2), 580-617, 2004. - (with C.-C. Chen and T. Yang) "Existence of boundary layer solutions to the Boltzmann equation"
,
*Anal. Appl. (Singap.)*, 2 (4), 337-363, 2004. - (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 (12), 1543-1608, 2004. - (with Yang, Tong; Yu, Shih-Hsien) "Energy method for Boltzmann equation"
,
*Phys. D*, 188 (3-4), 178-192, 2004. - (with Yu, Shih-Hsien) "Boltzmann equation: micro-macro decompositions and positivity of shock profiles"
,
*Comm. Math. Phys.*, 246 (1), 133-179, 2004. - (with T. Ruggeri) "Entropy production and admissibility of shocks"
,
*Acta Math. Appl. Sin. Engl. Ser.*, 19, 1-12, 2003. - (with Y. Deng, T. Yang, and T. Yao) "Solutions with vacuum for Euler-Poisson equations"
,
*Arch. Rational Mech. Anal.*, 164 (3), 261-285, 2002. - (with T. Yang) "Weak Solutions to General Systems of Hyperbolic Conservation Laws"
,
*Comm. Math. Phys.*, 230 (2), 289-327, 2002. - "Shock waves. Proceedings of the International Congress of Mathematicians"
,
*Higher Ed. Press (Beijing)*, III, 185-188, 2002. - (with T. Yang and Y. Zheng) "Some nonlinear functionals for scalar conservation laws"
,
*Methods Appl. Anal.*, 8 (4), 609-622, 2001. - "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.
- (with S.H. Yu) "145Hyperbolic conservation laws and dynamic systems"
,
*Discrete Contin. Dynam. Systems*, 6 (1), 143-145, 2000. - "L
_{1}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. - (with W.-C. Lien) "Nonlinear stability of a self-similar 3-dimensional gas flow"
,
*Comm. Math. Phys.*, 204 (3), 525-549, 1999. - (with W.-C. Lien) "Nonlinear stability of a self-similar 3-dimensional gas flow"
,
*Comm. Math. Phys.*, 204 (3), 525-549, 1999. - (with S.-H. Yu) "Nonlinear stability of weak detonation waves for a combustion model"
,
*Comm. Math. Phys.*, 204, 551-586, 1999. - (with T. Yang) "Well-posedness theory for hyperbolic conservation l aws, Comm. Pure Appl. Math. LII"
,
*Comm. Pure Appl. Math.*, II, 1553-1586, 1999. - (with S.-H. Yu) "Continuum shock profiles for discrete conservation laws, II. Stability. Comm. Pure Appl. Math. LII (1999), 1047-1073." , 1999.
- (with T. Yang) "A generalized entropy for scalar conservation laws"
,
*Comm. Pure Appl. Math.*, LII, 1427-1442, 1999. - (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.
- (with A. Bressan and T. Yang) "L1 stability estimates for nxn conservatiob laws"
,
*Archive Rational Mech. Anal.*, 1998. - (with SIAM J. Math. Anal.) "Behaviours of solutions for the Burgers equation with boundary corresponding to rarefaction waves"
,
*A. Matsumura and K. Nishihar*, 29, 293-308, 1998. - (with T. Yang) "L1 stability of conservation laws with coinciding Hugoniot and characteristic curves"
,
*Indiana Univ. Math. J.*, 1998. - (with T. Yang) "(with ) L1 stability of 2x2 systems of hyperbolic conservation laws"
,
*J. Amer. Math. Soc.*, 729-772, 1998. - (with Z. Xin and T. Yang) "Vacuum states for compressible flow"
,
*Disc. Cont. Dyn. Ana.*, 4, 1-32, 1998. - "Zero dissipation and stability of shock waves"
,
*Methods and Appl. Analysis*, 5, 81-94, 1998. - (with W. Wang) "The pointwise estimates of diffusion wave for the Navier-Stokes systems in odd dimensions"
,
*Comm. Math. Phys.*, 196, 145-173, 1998. - (with S.-H. Yu) "Continuum shock profiles for discrete conservation laws, I. Construction"
,
*Comm. Pure Appl. Math.*, 1998. - (with Y. Zeng) "Compressible Navier-Stokes equations with zero heat conductivity"
,
*J. D. E.*, 1998. - "Regularization of solution operators for quasilinear hyperbolic-parabolic partial differential equations"
,
*J. Partial Differential Equations*, 10 (4), 347-354, 1997. - (with T. Yang) "L1 stability of constant states for hyperbolic conservation laws"
,
*Methods and Appl. Analysis*, 4, 339-355, 1997. - (with K. Nishihara) "Asymptotic behaviour for scalar viscous conservation law with boundary effect"
,
*J.D.E.*, 133, 296-320, 1997. - (with Z. Xin) "Pointwise decay to contact continuities for viscous conservation laws"
,
*Asian J. Math.*, 1, 34-84, 1997. - (with T. Yang) "Compressible Euler equations with vacuum"
,
*J.D.E.*, 140, 223-237, 1997. - "Pointwise convergence to shock waves for viscous conservaton laws, Comm. Pure Appl. Math. L (1997)"
,
*Comm. Pure Appl. Math.*, L, 1113-1182, 1997. - (with S. Yu) "Propagation of Burgers stationary shocks under boundary effect"
,
*Archive Rational Mech. Anal.*, 139, 57-82, 1997. - (with Y. Zeng) "Large time behavior of solutions of general quasilinear hyperbolic-parabolic systems of conservation laws"
,
*Memoirs, Amer. Math. Soc.*, 599, 1997. - (with D. Li and D. Tan) "Stability of strong detonation travelling waves to combustion model"
,
*J. Math. Anal. Appl.*, 201, 516-531, 1996. - "Gas flows with damping and vacuum"
,
*Japan J. Indus. and Appl. Math.*, 13, 25-32, 1996. - "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.
- (with K. Zumbrum) "On nonlinear stability of general undercompressive viscous shock waves"
,
*Comm. Math. Phys.*, 175, 319-345, 1995. - (with K. Zumbrun) "Nonlinear stability of an undercompressive shock for complex Burgers equation"
,
*Comm. Math. Physics*, 168, 163-186, 1995. - (with L. Ying) "Nonliner stability strong detonations for a combustion model"
,
*SIAM J. of Math. Anal.*, 26, 519-528, 1995. - (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.
- "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. - (with G.-Q. Chen and D. Levermore) "Hyperbolic conservation laws with stiff relaxation terms and entropy"
,
*Comm. Pure Applied Math.*, 47, 787-830, 1994. - "Nonlinear evolutionary partial differential equations."
,
*Proceedings of the International Conference held in Beijing*, 21-25, 1993-06. - (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.
- "Nonlinear waves for viscous conservation laws"
,
*Nonlinear evolutionary partial differential equations*, 65-74, 1993. - (with L. Hsiao) "Nonlinear diffusive phenomena of nonlinear hyperbolic systems"
,
*Chin.Ann. Math.*, 14B, 465-480, 1993. - (with P. Le Floch) "Existence theory for nonlinear hyperbolic systems in nonconservative form"
,
*Forum Math.*, 5, 261-280, 1993. - (with H. Freistühler) "Nonlinear stability of overcompressive shock waves in a rotationally invariant system of viscious conservation laws"
,
*Comm. Math. Physics*, 153, 147-158, 1993. - (with G.-Q. Chen) "Zero relaxation and dissipation limits for hyperbolic conservation laws"
,
*Comm. Pure Appl. Math.*, 46, 755-781, 1993. - (with L. Hsiao) "(with ) Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping"
,
*Comm. Math. Phys.*, 143, 599-605, 1992. - (with Z. Xin) "Stability of viscous shock waves associated with a nonstrictly hyperbolic conservantion law, Comm. Pure Appl. Math., XLV (1992), 361-388." , 1992.
- "Interaction of nonlinear hyperbolic waves, Nonlinear Analysis"
,
*Academia Sinica, R.O.C., World Scientific*, 171-184, 1991. - "Nonlinear hyperbolic-parabolic p.d.e., Nonlinear Analysis"
,
*Academia Sinica, R.O.C., World Scientific*, 161-170, 1991. - "Viscosity criterion for hyperbolic conservation laws"
,
*Proc. SIAM. Ed. M. Shearer*, 1991. - (with T. Zheng) "A scalar combustion model"
,
*Arch. Rational Mech. Anal.*, 114, 297-312, 1991. - "On the viscosity criterion for hyperbolic conservation laws. Viscous profiles and numerical methods for shock waves (Raleigh, NC, 1990), 105-114." , 1990.
- (with S. Hsu) "Nonlinear singular Sturm-Liouville problem and application to transonic flow through a nozzle"
,
*Comm. Pure Appl. Math.*, 43, 31-61, 1990. - (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, 139-145, 1990. - "Nonlinear hyperbolic waves. Nonlinear hyperbolic equations in applied sciences. Rend. Sem. Mat. Univ. Politec. Torino 1988, Special Issue, 269--277 (1989)." , 1989.
- "Nonlinear analysis. Papers from the conference held in Taipei, June 19--24, 1989" , 1989.
- "Geometric theory of shock waves. Multidimensional hyperbolic problems and computations (Minneapolis, MN, 1989), 198-202." , 1989.
- (with D. Hoff) "The inviscid limit for the Navier-Stokes equations of compressible, instropic flow with shock data"
,
*Indiana Univ. J.*, 38, 861-915, 1989. - (with Hsu, Sze-Bi) "Local uniqueness of interior layer solution and its related stability property."
,
*Nonlinear analysis (Taipei)*, 51-60, 1989. - "Quasilinear hyperbolic-parabolic partial differential equations"
,
*Algebra, analysis and geometry (Taipei)*, 185-197, 1988. - (with Z. Xin) "Nonlinear stability of rarefaction waves for compressible Navier--Stokes equations"
,
*Comm. Math. Phys.*, 451-465, 1988. - "Nonlinear waves for viscoelasticity with fading memory"
,
*J. Diff. Equ.*, 76, 26-46, 1988. - "Nonlinear resonance for quasilinear hyperbolic equation"
,
*J. Math. Phys.*, 28, 2593-2602, 1987. - "Hyperbolic conservation laws with relaxation"
,
*Comm. Math. Phys.*, 108, 153-175, 1987. - "Pointwise convergence to $N$-waves for hyperbolic conservation laws"
,
*Bulletin, Inst. Math., Academia Sinica*, 15, 1-17, 1987. - "Hyperbolic conservation laws and related topics. Partial differential equations of hyperbolic type and applications, 113--139, World Sci. Publishing, Singapore, 1987." , 1987.
- (with I-L. Chern) "Convergence to diffusion waves of solutions for viscous conservation laws"
,
*Comm. Math. Phys.*, 110, 503-517, 1987. - (with R. Caflisch) "Stability of shock waves for the Broadwell equations"
,
*Comm. Math. Phys.*, 39, 565-594, 1986. - "Shock waves for compressible Navier-Stokes equations are stable"
,
*Comm. Pure Appl. Math.*, 39, 565-594, 1986. - (with L. P. Huang) "Piecewise steady elements and Godunov-type difference scheme for duct flow"
,
*Comp. & Maths. with Appls.*, 12A, 377-388, 1986. - "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.
- "Nonlinear stability of shock waves for viscous conservation laws, Memoirs"
,
*Amer. Math. Soc.*, 328, 1985. - "Nonlinear stability of shock waves for viscous conservation laws"
,
*Amer. Math. Soc. (N.S.)*, 12 (2), 233-236, 1985. - (with C. H. Wang) "On a system of nonstrictly hyperbolic system"
,
*J.D.E.*, 57, 1-14, 1985. - "Stability of nonlinear waves. Metastability and incompletely posed problems"
,
*Minneapolis, Minn.*, 259-267, 1985. - (with H. Galz) "The asymptotic analysis of wave interactions and numerical calculations of transonic nozzle flow"
,
*Advances Appl.*, 5, 111-146, 1984. - (with M. Pierre) "Source-solutions and asymptotic behavior in conservation law"
,
*J. Diff. Equ.*, 51, 419-441, 1984. - (with C. Li) "Asymptotic states for hyperbolic conservation laws with a moving source"
,
*Advances in Appl. Math.*, 4, 353-379, 1983. - "Resonance for quasilinear hyperbolic equation"
,
*Bulletin Amer. Math. Soc.*, 6, 463-465, 1982. - (with A. Chorin and Z. H. Teng) "Riemann problems for reacting gas with applications to transitions"
,
*SIAM J. Appl. Math.*, 42, 964-981, 1982. - "Nonlinear stability and instability of transonic flows through a nozzle"
,
*Comm. Math. Phys.*, 83, 243-260, 1982. - "Transonic gas flow in a duct of varying area"
,
*Arch. Rat. Mech. and Anal.*, 80, 1-18, 1982. - "Admissible solutions of hyperbolic conservation laws, Memoirs"
,
*Amer. Math. Soc.*, 240, 1981. - (with Conlon, Joseph G.) "Admissibility criteria for hyperbolic conservation laws"
,
*Indiana Univ. Math. J.*, 30 (5), 641-652, 1981. - (with J. Smoller) "On the vacuum state for isentropic gas dynamics equations"
,
*Advances in Math.*, 1, 345-359, 1980. - "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.
- "A system of quasilinear hyperbolic partial differential equations. Trends in applications of pure mathematics to mechanics, Vol. III (Edinburgh, 1979), 179-189." , 1979.
- "Quasilinear hyperbolic systems68"
,
*Comm. Math. Phys.*, 68, 142-172, 1979. - "Development of singularities in the nonlinear waves for quasilinear hyperbolic partial differential equations"
,
*J. Diff. Equations,*, 33, 92-111, 1979. - (with S. Antman) "Traveling waves in hyperelastic rods"
,
*Quarterly of Appl. Math.*, 36, 377-399, 1979. - "The free piston problem for gas dynamics"
,
*J. of Diff. Equations*, 39, 175-191, 1978. - "Invariants and asymptotic behavior of solution of a conservation law"
,
*Proceedings of A.M.S.*, 71, 227-231, 1978. - "Asymptotic behavior of solutions of general systems of nonlinear hyperbolic conservation laws"
,
*Indiana Univ. J.*, 27, 211-253, 1978. - "The deterministic version of the Glimm scheme"
,
*Comm. Math. Phys.*, 57, 135-148, 1977. - "Linear and nonlinear large-time behaviors of solutions of hyperbolic conservation laws"
,
*Comm. Pure Appl. Math.*, 30, 767-796, 1977. - "Large-time behavior of solutions of initial and initial-boundary value problem of general system of hyperbolic conservation laws"
,
*Comm. Math. Phys.*, 55, 163-177, 1977. - "Decay to N-waves of solutions of general systems of nonlinear hyperbolic conservation laws"
,
*Comm. Pure Appl. Math*, 30, 586-611, 1977. - "Initial-boundary value problems for gas dynamics"
,
*Arc. Rat. Mech. and Anal.*, 64, 137-168, 1977. - "Solutions in the large for equations of nonisentropic gas dynamics"
,
*Indiana Univ. J.*, 26, 144-177, 1977. - "The entropy condition and the admissibility of shocks"
,
*J. of Math. Anal. and Applications*, 53, 75-88, 1976. - "Shock waves in nonisentropic gas flow"
,
*J. Diff. Equations*, 22, 442-452, 1976. - "Uniqueness theorem of the Cauchy problem for general 2 X 2 conservation laws"
,
*J. Diff. Eqs.*, 20, 369-388, 1976. - "Existence and uniqueness theorems for Riemann problems"
,
*Transactions of A.M.S.*, 212, 375-382, 1975. - "The Riemann Problem for general systems of conservation laws"
,
*J. Diff. Equations*, 18, 218-234, 1975. - "The Riemann problem for general 2 X 2 conservation Laws"
,
*Transactions of A.M.S.*, 199, 89-112, 1974. - (with S. Cox) "Zero-memory limit for a viscoelasticity model with Riemann data (preprint)."

Director & Deputy Director