[102] Shock wave interactions in general relativity: The geometry behind metric smoothing and the existence of locally inertial frames,

submitted.

[101] An instability in the standard model of cosmology creates the anomalous acceleration without dark energy,

November 22, 2017, RSPA.[101A]

[100] Causal dissipation for the fluid dynamics of ideal gases,

April 19,2017, RSPA. [101]

[99] Numerical analysis of a canonical shock wave interaction problem in general relativity,

April 2015, Special issue in honor of Tai-Ping Liu’s seventieth birthday, Bulletin of the Institute of Mathematics, Academia Sinica,Taiwan.

[98] Regularity singularities and the scattering of gravity waves in approximate locally inertial frames, Meth. Appl. Anal, Vol. 23, No. 2, pp. 233–258, September 2016.

[97] An alternative proposal for the anomalous acceleration,

Surveys in Differential Geometry, Vol. 20 (2015): One Hundred Years of General Relativity, eds S.T. Yau and L. Bieri.

[96] No regularity singularities exist at points of general relativistic shock wave interaction between shocks from different characteristic families,

May 17, 2015, RSPA.

[95] Causal dissipation and shock profiles in the relativistic fluid dynamics of pure radiation,

March 20, 2014, RSPA.

[94] Subluminality and damping of plane waves in the causal dissipation of relativistic fluid dynamics,

preprint July, 2013.

[93] Corrections to the Standard Model of Cosmology,

Communications in Information and Systems (CIS), (invited submission in honor of Marshall Slemrod's 70th birthday), [submitted September 2013].

[92] A Nash-Moser framework for finding periodic solutions of the compressible Euler equations,

Journal of Scientific Computing, April 2, 2014 (Springer)

[92] A Nash-Moser framework for finding periodic solutions of the compressible Euler equations,

Proceedings of Waterloo 2013, Presented by Robin Young, (Preprint)

[91] A canonical small divisor problem for the Nash-Moser Method,

Communications in Information and Systems (CIS), (invited submission in honor of Marshall Slemrod's 70th birthday), [submitted September 2013].

[90] Causal dissipation and shock profiles in the relativistic fluid dynamics of pure radiation,

preprint July, 2012.

[89] On viscosity and heat conduction for the relativistic fluid dynamics of pure radiation,

preprint December, 2011.

[88] A proof of convergence for the numerical approximations generated by the locally inertial Godunov method in general relativity,

preprint.

[87] Nash-Moser for Euler Newton,

preprint.

[86] Points of general relativistic shock wave interaction are "regularity singularities" where space-time is not locally flat,

Replaced by [96].

[85] A One Parameter Family of Expanding Wave Solutions of the Einstein Equations that induce an Anomalous Acceleration into the Standard Model of Cosmology,

AMS/IP Studies in Advanced Mathematics Volume 51, 2011.

[84] Simulation of general relativistic shock waves by a locally inertial Godunov method featuring dynamic time dilation

Proc. Roy. Soc. A, Published online, 4 April 2012, doi: 10.1098/rspa.2011.0355.

[83] The ``Big Wave'' Theory for Dark Energy

Proceedings: Quantum Field Theory and Gravity, Regensberg, Germany, Sept. 28-August 1, 2010.

[82] General Relativistic Self-Similar Waves that induce an Anomalous Acceleration into the Standard Model of Cosmology

Memoirs of the AMS, November 3, 2011; S 0065-9266(2011)00641-6.

[81] Answers to Questions Posed by Reporters

(Supplement to [80], prepared August 19, 2009.)

[80] Expanding wave solutions of the Einstein equations that induce an anomalous acceleration into the Standard Model of Cosmology

PNAS, Vol.106, no.34, 2009, pp. 14218-14218.

[79] A Liapunov-Schmidt Reduction for Time-Periodic Solutions of the Compressible Euler Equations

Meth. Appl. Anal., Vol. 17, No. 3, pp. 225-262, September 2010.

[78] Time periodic linearized solutions of the compressible Euler equations and a problem of small divisors

SIAM J. Math. Anal., Vol. 43, No. 1, 2011, pp. 1-49.

[77] Periodic Solutions of the Euler Equations: A paradigm for time-periodic sound wave propagation in the compressible Euler equations

Meth. Appl. of Anal. Vol. 16, No.3 pp. 341-364, September 2009.

[76] Linear waves that express the simplest possible periodic structure of the compressible Euler equations

Acta Mathematica Scientia, Vol. 29, Ser. B, no. 6, 2010, pp. 1749-1766.

[75] Shock wave interactions in general relativity: a locally inertial Glimm scheme for spherically symmetric spacetimes

Springer, 2007, VIII, ISBN: 978-0-387-35073-8.

Pre-publication Manuscript

[74] A Proposal to Numerically Simulate a Cosmic Shock Wave by Use of a Locally Inertial Glimm Scheme

Abstracts of the AMS, Numerical Relativity, AMS New Orleans, 2007. (Beginning of program to simulate GR expanding waves.)

[73] A Shock Wave Cosmology

Patrika: Newsletter of the Indian Academy of Sciences, No. 43, pp 8-9, March 2006.

[72] Shock wave cosmology inside a Black Hole: A computer visualization

Hyperbolic Problems: Theory, Numerics and Applications, Vol. 1, Yokahama Publishers (2006) pp. 57-67.

Color Preprint

[71] How inflation is used to resolve the flatness problem

Jour. of Hyp. Diff. Eqns., Vol. 3, no. 2, 2006, pp. 375-386.

Preprint

[70] A shock wave refinement of the Friedmann Robertson Walker spacetime

Encyclopedia of Mathematical Physics, Elsevier, 2006.

Preprint

[69] How inflationary spacetimes might evolve into spacetimes of finite total mass

Methods and Applications of Analysis, Vol. 12, No. 4, 2005, pp. 451-464.

[68.5] The Hubble length as a critical length scale in shock wave cosmology

Proceedings from Conference on Analysis, Modeling, Computation and Multi-phase flow (in honor of James Glimm's 70th birthday)--Stony Brook, August 2004.

[68] Shock waves and cosmology

Third International Conference of Chinese Mathematicians, Chinese University of Hong Kong, 2004.

[67] Shock wave cosmology inside a black hole: The case of non-critical expansion

Hyperbolic Differential Equations, Vol. 1, 2004, pp.429-443.

Journal

[66] A bound on the total variation of the conserved quantities for solutions of a general resonant nonlinear balance law

SIAM J. Appl. Math.,Vol. 64, No. 3, 2004, pp. 819-857.

[65] Cosmology, Black Holes, and Shock Waves beyond the Hubble Length

Meth. and Appl. of Anal., Vol. 11, No. 1, 2004, pp. 077-132.

[64] Shock-wave solutions of the Einstein equations: Existence and consistency by a locally inertial Glimm Scheme

Memoirs of the AMS, Vol. 172, No. 813, November 2004.

Pre-publication Notes

[63] The generic solution of the Riemann problem in a neighborhood of a point of resonance for systems of nonlinear balance laws

Methods and Applications of Analysis, Vol. 10, No. 2, 2003, pp. 279-294.

[62] Shock-wave cosmology inside a black hole

PNAS, Vol. 100, no. 20, 2003, pp. 11216-11218.

[61] Solving the Einstein equations by Lipschitz continuous metrics: Shock waves in General Relativity

Handbook of Mathematical Fluid Dynamics, 2003, (series by Elsevier).

[60] A locally inertial Glimm scheme for General Relativity

Seventh Workshop on Partial Differential Equations, Mathematica Contemporanea, Vol. 22, 2002, pp. 163-179.

[59] A shock-wave formulation of the Einstein equations

Methods and Applications of Analysis, Vol. 7, no. 4, 2000, pp. 793-812.

[58] Shock-wave cosmology

AMS/Advanced Mathematics, Vol. 16, 2000, pp. 351-359.

[57] Cosmology with a Shock-Wave

Comm. Math. Phys., Vol. 210, no. 2, 2000, pp. 275-308.

[56] Theory of a Cosmic Shock Wave

Meth. Appl. of Anal., Vol. 8, no. 4, 2001, pp. 599-608.

[55] Shock-wave solutions of the Einstein equations: A general theory with examples

Proceedings of European Union Research Network's 3rd Annual Summerschool, Lambrecht (Pfalz) Germany, May 16-22, 1999.

[54] Applications of shock-waves in general relativity

Proceedings of the VII Int'l Conf. on Hyperbolic Problems, Theory, Numer. and Appl., ETH Zurich, February, 1998.

[53] On the Oppenheimer-Volkov equations in general relativity

Arch. Rat. Mech. Anal., Vol. 142, 1998, pp. 177-191.

[52] Shock-wave solutions in closed form and the Oppenheimer-Snyder limit in general relativity

SIAM J. Appl. Math, Vol. 58, No. 1, 1998, pp. 15-33.

[51] Shock-waves near the Schwarzschild radius and the stability limit for stars

Physical Review D, Vol. 55, No. 12, 1997 pp. 7518-7528.

[50] Solutions of the Oppehheimer-Volkoff equations inside 9/8'ths of the Schwarzschild radius

Comm. Math. Phys., Vol. 184, 1997, pp. 597-617.

[49] Multi-dimensional shock-waves for relativistic fluids

AMS/IP Studies in Advanced Mathematics, Vol. 3, 1997, pp. 377-391.

[48] Shock-waves in general relativity

Harmonic Analysis and Nonlinear Differential Equations: A Volume in Honor of Victor Shapiro, M. L. Lapidus, L. H. Harper and A. J. Rumbus, Editors, Contemporary Mathematics, Vol. 208, 1997.

[47] General relativistic shock-waves that extend the Oppenheimer-Snyder model

Arch. Rat. Mech. Anal., Vol. 138, 1997, 239-277.

[46] The large time stability of sound waves

Comm. Math. Phys, Vol. 179, 1996, pp. 417-466.

[45] Solutions to the Euler Equations with Large Data

Hyperbolic Problems: Theory, Numerics, Applications, 1996, p. 258-267.

[44] Shock-Waves and irreversibility in Einstein's theory of gravity

Hyperbolic Problems: Theory, Numerics, Applications, 1996, pp. 81-90.

[43] Shock-wave explosions in general relativity

Journees Equations Aux Derivees Partielles, Saint-Jean-De-Monts, XVII, 1995, pp. 1-20.

[42] The large time existence of periodic solutions for the compressible Euler equations

Contemporanea Mathematica, IMPA, 1995, (Proceedings of the Fourth International Workshop on PDE).

[41] Astrophysical shock wave solutions of the Einstein equations

Phys. Rev. D, Vol. 51, No. 6, 1995 pp. 2733-2743.

[40] Suppression of oscillations in Godunov's method for a resonant non-strictly hyperbolic system

SIAM J. Numer. Anal., Vol. 32, No. 3, June 1995.

[39] Convergence of the 2x2 Godunov method for a general resonant nonlinear balance law

SIAM Jour. Appl. Math. Vol. 55, No. 3, 1995 pp. 625-640.

[38] A comparison of convergence rates for Godunov's method and Glimm's method

SIAM J. Numer. Anal., Vol. 32, No. 3, 1995, pp. 824-840.

[37] Shock-waves in general relativity- A generalization of the Oppenheimer-Snyder model for gravitational collapse

Nonlinear PDE and their applications, College de France, Seminar Vol. {\bf X}, 1994.

[36] Shock Waves and General Relativity

Journees Equations Aux Derivees Partielles, Saint-Jean-De-Monts, June 1994.

[35] Shock-wave solutions of the Einstein equations: The Oppenheimer-Snyder model of gravitational collapse extended to the case of non-zero pressure

Arch. Rat. Mech. Anal., Vol. 128, 1994, pp 249-297.

[34] Multi-dimensional shock waves for relativistic fluids

Proceedings of Conference on Shock Waves and Conservation Laws, Beijing, China, June, 1993.SIAM J. Numer. Anal.,\\\> Vol. 32, No. 3, June 1995.

[33] Global solutions of the relativistic Euler equations

Comm. Math. Phys., Vol. 156, 1993, pp. 67-99.

[32] Nonlinear resonance in systems of conservation laws

SIAM Jour. Appl. Math., Vol. 52, No. 5, 1992, pp. 1260-1278.

[31] Multiphase flow models with singular Riemann problems

Computational and Applied Mathematics, Vol. 11, 1992, pp. 147-167.

[30] From Newton to Einstein

American Mathematica Monthly (Cover article), Vol. 99, No. 6, 1992, pp. 507-521.

[29] On the convergence of Glimm's method and Godunov's method when wave speeds coincide

Proceedings of the Second International Conference on PDE, May 15-18, 1991.

[28] On blowup in a resonant nonstrictly hyperbolic system

Matematica Contemporanea, IMPA, Vol. 3, 1991, pp. 67-89.

[27] Supnorm estimates in Glimm's method

J. Diff. Eqs., Vol. 83, No.1, 1990, pp. 79-84.

[26] A connection for Fermi Transport in the theory of general relativity

Davis preprint.

[25] Nonlinear resonance in inhomogeneous systems of conservation laws

Contemporary Mathematics,Vol 108, 1990, pp. 63-77,

[24] Instability of rarefaction shocks for systems of conservation laws

Arch. Rational Mech. Anal., Vol. 112, 1990, pp. 63-81.

[23] Weak stability in the global L^1-norm for systems of hyperbolic conservation laws

Trans. Am. Math. Soc., Vol. 317, No. 2, 1990, pp. 673-685.

[22] The structure of asymptotic states in a singular system of conservation laws

Adv. Appl. Math., Vol. 11, pp. 205-219 (1990)

[21] The L^1-norm distinguishes the strictly hyperbolic from the non-strictly hyperbolic theory of the initial value problem for systems of conservation laws

Notes on Numerical Fluid Mechanics, Vol. 24, 1988, pp. 608-616.

[20] A characterization of the weakly continuous polynomials in the method of compensated compactness

Trans. Am. Math. Soc., Vol. 310, No. 1, 1988, pp. 405-417.

[19] Classification of quadratic Riemann problems III

SIAM Jour. Appl. Math. Vol.48, No.6, 1988, pp. 1302-1318.

[18] Classification of quadratic Riemann problems II

SIAM Jour. Appl. Math. Vol.48, No.6, 1988, pp.1287-1301.

[17] The Riemann problem near a hyperbolic singularity: the classification of solutions of quadratic Riemann problems I

SIAM Jour. Appl. Math. Vol.48, No. 5, 1988, pp. 1009-1032.

[16] On the role of the characteristic set in the method of compensated compactness

Davis Preprint

[15] On weak continuity and the Hodge decomposition

Trans. Am. Math. Soc., Vol. 303, No. 2, 1987, pp. 609-618.

[14] Continuous dependence in systems of conservation laws

Atlas Do Decimo Quinto Coloquio Brasileiro de Matematica, (Proceedings of the Brazilian Math. Society), 1987, pp. 67-83.

[13] Degenerate systems of conservation laws

Contemporary Mathematics, Vol. 60, 1987, pp 125-133.

[12] Stability and decay in systems of conservation laws

Proceedings of the First International Conference on Hyperbolic Problems, Springer 1986

[11] Decay with a rate for noncompactly supported solutions of conservation laws

Trans. Am. Math. Soc., Vol. 298, No.1, 1986, pp. 43-82.

[10] Analysis of a singular hyperbolic system of conservation laws

Jour. Diff. Eqs., Vol.65, No.2., 1986, pp 250-286.

[9] Examples and classification of non-strictly hyperbolic systems of conservation

Abstracts of AMS, January 1985.

[8] Stability of Godunov's method for a class of 2x2 systems of conservation laws

Trans. Amer. Math. Soc., Vol. 288, No.1, 1985, pp. 115-123.

[7] No L^1 contractive metrics for systems of conservation laws

Trans. Amer. Math. Soc., Vol. 288, No.2, 1985, pp. 471-480.

[6] Systems of conservation laws with invariant submanifolds

Trans. Amer. Math. Soc., Vol 280, No. 2, 1983, pp. 781-795.

[5] Systems of conservation laws with coinciding shock and rarefaction waves

Contemporary Mathematics, Vol. 17, 1983, pp. 141-151.

[4] The existence of a global weak solution of the waterhammer problem

Comm. Pure Appl. Math. Vol. 35, 1982, pp. 697-735.

[3] Global solution of the Cauchy problem for a class of 2x2 non-strictly hyperbolic conservation laws

Adv. Appl. Math. 3, 1982, pp. 335-375.

[2] Stability and error bounds for a fractional step scheme to compute weak solutions to the waterhammer problem

Presented at the University of Maryland, Feb. 6, 1981.

[1] Solutions in the large for the nonlinear hyperbolic conservation laws of gas dynamics

Jour. Diff. Eqs., Vol 41, No.1, July 1981, pp. 96-161.