Name: Ralph Saxton (Prof)
Affiliation: Department of Mathematics, University of
New Orleans, Lakefront, New Orleans, LA 70148
Degree: PhD (Mathematics, 1981) Heriot-Watt
Phone: (504) 280-6130
Fax: (504) 280-5516
Department: http://www.math.uno.edu/ Faculty:
Research Interests: Incompressible fluids, solids, liquid crystals,
quasilinear hyperbolic-parabolic systems, elliptic equations.
(Blow-Up of Solutions to the Generalized Inviscid Proudman-Johnson Equation,
Abeer Yasin (Multiple Solutions on a Ball for a Generalized Lane-Emden Equation,
An H^1 model for inextensible strings with S.
Preston (Discrete and Continuous Dynamical System - Series A, 2012/3).
Heat propagation with phase transitions in low temperature solids, with K.
Saxton, " Trends in Applications of Mathematics to Mechanics", STAMM
2004, Shaker-Verlag, 463-472 (2005).
Phase transitions and aspects of heat propagation in low temperature
solids, with K. Saxton, EQUADIFF 2003, World Scientific, 1128-1130 (2005).
Some Effects of Phase Transitions on Heat Propagation, with K. Saxton,
Arch. Mech., 54, 5-6 (2002).
Nonlinear PDEs, Dynamics and Continuum Physics, with J. Bona and K. Saxton
(editors), American Mathematical Society (2000). MR2000m:35003
Nonlinearity and memory effects in low temperature heat propagation, with
K. Saxton, Arch. Mech., 52, 1 (2000).
On second sound at the critical temperature, with K. Saxton and W. Kosinski, Quart. Appl. Math., LVII, 4, 723-740 (1999).
Second Sound Speed in a Crystal of NaF at Low
Temperature, with W. Kosinski and K. Saxton, Arch.
Mech., 49, 1, 189-196 (1997).
Nonstrictly Hyperbolic Systems of Partial
Differential Equations, with V. Vinod, "Recent Developments in Evolution
Equations", Pitman Research Notes in Mathematics, 324, 239-243, Longman
(1995). MR1 417 07
On second sound at the critical temperature, with W. Kosinski
and K. Saxton, Society of Engineering Science, 32nd Annual Meeting, 505-506
Blow Up at the Boundary of Solutions to Nonlinear Evolution Equations,
"Evolution Equations", Lecture Notes in Pure and Applied Mathematics,
168, 383-392 (1994). MR95i:35025
Radial Solutions to a Nonlinear p-Harmonic Dirichlet
Problem, with D. Wei, Applic. Anal., 51, 1-4, 59-80
Formation of Singularities for a Class of Nonlinear, Hyperbolically
Degenerate Initial-Boundary Value Problems, Appl. Math. Lett., 5, 3, 73-75
Finite Time Boundary Blowup for a Degenerate, Quasilinear Cauchy Problem,
"Partial Differential Equations", Pitman Research Notes in
Mathematics Series, 273, 212-215, Longman (1992).
Dynamics of Director Fields, with J. Hunter, SIAM J. Appl. Math., 51, 6, 1498-1521
Instability of the Liquid Crystal Director, Contemporary Mathematics, 100,
325-330 (1989). MR90k:35246
The Equations of Incompressible Elasticity, with D. Ebin,
Contemporary Mathematics, 60, 25-34 (1987). MR88a:73034
Solitary Wave Interaction in Elastic Rods, with P. Clarkson and R. LeVeque, Stud. Appl. Math. LXXV, 2, 95-123 (1986).
The Initial-Value Problem for Elastodynamics of
Incompressible Bodies, with D. Ebin, Arch. Rat. Mech.
Anal. 94, 1, 15-38 (1986). MR87h:58028
Existence of Solutions for a Finite Nonlinear Hyperelastic
Rod, J. Math. Anal. Appl. 105, 1, 15-38 (1985). MR86m:3511
The Cauchy and Backward Cauchy Problem for a Nonlinear Hyperelastic/Viscoelastic
Infinite Rod, Lecture Notes in Mathematics, 1032, Springer Verlag
Solitary and Travelling Waves in a Rod, Lecture Notes in Mathematics, 964,
Springer Verlag (1982). MR84j:35150
The Nonlinear Pochhammer-Chree Equation, PhD
thesis, Heriot-Watt University (1981).
Science, Math, and Engineering Career Resources
Some mathematical resources
Collected Journal Links
Project Euclid Digital
Library Math Collection
Electronic Journal of Differential
Electronic Library of Mathematics
European Mathematical Society
IMU - International Mathematical Union
Mathematical Physics Archive
Trondheim: Conservation Laws PreprintServer
American Mathematical Society journals
Bulletin of the AMS
Conformal Geometry and Dynamics
Electronic Research Announcements
Journal of the AMS
Mathematics of Computation
Notices of the AMS
Proceedings of the AMS
Transactions of the AMS
Oxford University Press
IMA Journal of Applied Mathematics
IMA Journal of Numerical Analysis
Proceedings of the Edinburgh
The Quarterly Journal of
The Quarterly Journal of Mechanics
and Applied Mathematics
Journal of Mathematics
de l'Institut Fourier
Geometry and Topology
J. fur die reine
und angewandte Mathematik (Crelle's Journal)
J. Mathematical Physics
Journal of Group Theory
Journal of Nonlinear Science
Journal of Number Theory
New York Journal of
Pacific Journal of Mathematics
Regular and Chaotic
Dynamics Home Page
Annals of Mathematics
Journal of Symbolic Logic
Journal of the American
Mathematics of Computation
Proceedings of the American
SIAM Journal on Applied
SIAM Journal on Numerical
the American Mathematical Society
it often happens that scientists say, 'You know that's a really good argument;
my position is mistaken,' and then they actually change their minds and you
never hear that old view from them again. They really do it. It doesn't happen
as often as it should, because scientists are human and change is sometimes
painful. But it happens every day. I cannot recall the last time something like
that happened in politics or religion.
Sagan, 1987 CSICOP keynote address
I don't see how anybody understands what is happening in
physics today. Even I don't understand much which I would like to learn from
physics books. But with me, if I don't understand something, then I go to the
telephone and call up Debye or Born, and they come and explain it to me. And
then I understand it -- but what do other people do?
I was always delighted by the way in which Thom discussed
mathematics, using sentences obviously having no strict logical meaning at all.
While I was never able to completely free myself from the straitjacket of
logic, I was forever poisoned by the dream of the irresponsible mathematical
speculation with no exact meaning. "One can always find imbeciles to prove
theorems" was, according to Thom's students, his principle.
David Hilbert, quoted in Constance Reid's
biography of Hilbert
from "An Interview
with Vladimir Arnol'd"