PUBLICATIONS-Blake Temple
[103] Causal Dissipation in the relativistic dynamics of barotropic fluids, Jour Math Phys, 2018.
[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.
PDF
[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.