Publications | Other Significant Publications
Viscosity matrices for two-dimensional nonlinear hyperbolic systems, (with C. Conley), Comm. Pure Appl Math, 23, (1970), 867-884.
Solutions in the large for some nonlinear conservation laws, (with T.Nishida), Comm. Pure Appl. Math, 26, (1973) 183-200.
Wave front sets and the viscosity method, (with M. Taylor), Bull. Amer. Math Soc, 79, (1973), 431-436.
Mixed problems for nonlinear conservation laws, (with T. Nishida), J. Diff. Eqns, 23, (1977), 244-269.
Diffusion and the classical ecological interactions, (with E. Conway), Nonlinear Diffusion, Pitman Research Notes in Math, 14, (1977), 53-69.
Large time behavior of systems of nonlinear reaction-diffusion equations, (with E. Conway and D. Hoff), SIAM J. Appl. Math, 35, (1978), 1-16.
Topological techniques in reaction-diffision equations, (with C. Conley), Springer Notes in Biolog. Math, 38, (1980), 473-483.
A class of convergent finite difference schemes, (with T. Nishida), Comm. Pure Appl. Math,36, (1983), 785-808.
Existence, uniqueness, and non-degeneracy of positive solutions of semilinear elliptic equations, (with A. Wasserman), Comm. Math. Phy, 95, (1984), 129-159.
Symmetry-breaking for solutions of semilinear elliptic equations with general boundry conditions, (with A. Wasserman), Comm. Math. Phys, 105, (1986), 415-441.
Symmetry, degeneracy, and universality in semilinear elliptic equations, (with A. Wasserman), J. Func. Anal, 89, (1989), 364-409.
Existence of black hole solutions of the Einstein-Yang/Mills equations, (with A. Wasserman), Comm. Math. Phys, 154, (1993), 377-401.
Global solutions of the relativistic Euler equations, (with B. Temple), Comm. Math. Phys, 156, (1993), 67-99.
Shock wave solutions of the Einstein equations, (with B. Temple), Arch. Rat. Mech. Anal, 128, (1993), 249-297.
Solutions of the Oppenheimer-Volkoff equations inside 9/8ths of the Schwarzschild radius, (with B. Temple), Comm. Math. Phys, 184, (1997), 597-617.
Shock waves near the Schwarzchild radius and the stability limit for stars, (with B. Temple), Physical Review D, 55,(1997), 7518-7528.
Extendability of solutions of the Einstein-Yang/Mills equations (with A. Wasserman), Comm. Math. Phys, 194, (1998), 707-732.
The coupling of gravity to spin and electromagnetism, (with F. Finster, and ST Yau), Modern Physics Letters, (14), (1999), 1053-1057. THIS PAPER GOT HONORABLE MENTION , 4th PRIZE, IN THE GRAVITY RESEARCH FOUNDATION CONTEST.
The interaction of Dirac particles with non-abelian gauge fields and gravity—black holes, (with F. Finster and ST Yau), Michigan Math. J., 47, (2000), 199-208.
Non-existence of time-periodic solutions of the Dirac equation in an axi-symmetric black hole geometry, (with F.Finster, N. Kamran, and ST Yau), Comm.Pure Appl. Math, 53, (2000), 902-927.
Non-formation of vacuum states for the compressible Navier-Stokes equations, (with D. Hoff), Comm. Math. Phys, 216, (2001), 255-276.
The long-time dynamics of Dirac particles in the Kerr-Newman black hole geometry, (with F.Finster, N.Kamran and ST Yau), Adv. Theor.Math.Phys, 7, (2003), 25-52.
Rotating fluids with self-gravitation in bounded domains, (with T. Luo), Arch. Rat. Mech. Anal), 173, (2004), 345-377.
Cosmology, black holes, and shock waves beyond the Hubble distance, (with B. Temple), Methods and Appl. of Anal, 11, (2004), 77-133.
An integral spectral representation of the propagator for the wave equation in the Kerr geometry, (with F.Finster, N.Kamran, and ST Yau), Comm. Math. Phys, 260, (2005), 257-298.
Blowup of smooth solutions for the relativistic Euler equation, (with R. Pan), Comm. Math. Phys, 282, (2006), 729-755.
Decay of solutions of the wave equation in the Kerr Geometry, (with F.Finster, N.Kamran, and ST Yau), Comm. Math. Phys, 264, (2006), 465-503.
BOOK: Shock Waves and the Initial-Value Problem in General Relativity, (with B. Temple and J. Groah), Springer Monographs in Mathematics, Springer-Verlag, (2007).
Nonlinear stability of Newtonian rotating and non-rotating white dwarf and supermassive stars, (with T. Luo), Comm. Math. Phys, 284, (2008), 425-457.
Existence and nonlinear stability of rotating star solutions of the compressible Euler-Poisson equations, (with T. Luo), Arch. Rat. Mech. Anal, 191, 447-496.
Linear stability of the Teukolsky Equation for Higher Spin in the Schwarzschild Geometry(with F.Finster), Adv. Theor.Math. Phys, 13, (2009), 71-110.
A rigorous treatment of energy extraction from a rotating black hole, (with F. Finster, N. Kamran, and ST Yau), Comm. Math. Phys, (2009), 287, 829-947.
Linear waves in the Kerr geometry: a mathematical voyage to black hole physics, (with F.Finster, N.Kamran, and ST Yau), Bull Amer. Math. Soc, 46, 635-660.
Error Estimates for Approximate Solutions of the Riccoti Equation with Real or Complex Potentials, (with F. Finster), Arch. Rat. Mech. Anal, 197, 985-1109.
A One Parameter Family of Expanding Wave Solutions of the Einstein Equations That Induces an Anomalous Acceleration into the Standard Model of Cosmology, (with B. Temple), submitted.
General Relativistic Self-Similar Waves that Induce an Anomalous Acceleration into The Standard Model of Cosmology, (with B. Temple), Memoirs of the Amer. Math. Soc. (to appear).