Name: Ralph Saxton (Prof)
Affiliation: Department of Mathematics, University of New Orleans, Lakefront, New Orleans, LA 70148
Degree: PhD (Mathematics, 1981) Heriot-Watt University
Phone: (504) 280-6130
Fax: (504) 280-5516
Department: http://www.math.uno.edu/ Faculty: http://www.uno.edu/cos/mathematics/faculty/index.aspx
Research Interests: Incompressible fluids, solids, liquid crystals, quasilinear hyperbolic-parabolic systems, elliptic equations.
Doctoral Students:
Alejandro Sarria
(Blow-Up of Solutions to the Generalized Inviscid Proudman-Johnson Equation,
2012)
Abeer Yasin (Multiple Solutions on a Ball for a Generalized Lane-Emden Equation,
2008)
Publications/preprints:
Blow-up of solutions to the generalized inviscid Proudman-Johnson equation with A. Sarria (Journal of Mathematical Fluid Mechanics, 2012/3).
An H^1 model for inextensible strings with S. Preston (Discrete and Continuous Dynamical System - Series A, 2012/3).
On the Influence of Damping in Hyperbolic Equations with Parabolic Degeneracy with K. Saxton (Quart. Appl. Math., 2012)
Global Existence of Some Infinite Energy Solutions for a Perfect Incompressible Fluid with F. Tiglay (SIAM J. Math. Anal., 2008)
Phase Transitions and Change of Type in Low-Temperature Heat Propagation with K. Saxton (SIAM J. Appl. Math., 2006)
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). MR2000h:35158
Second Sound Speed in a Crystal of NaF at Low Temperature, with W. Kosinski and K. Saxton, Arch. Mech., 49, 1, 189-196 (1997).
Singularity Formation in Systems of Nonstrictly Hyperbolic Equations, with V. Vinod, Elec. J. Diff. Eq., 9, 1-15 (1995). MR96g:35118
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 (1995).
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 (1993). MR95e:35079
Formation of Singularities for a Class of Nonlinear, Hyperbolically Degenerate Initial-Boundary Value Problems, Appl. Math. Lett., 5, 3, 73-75 (1992). MR93d:35104
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 (1991). MR93a:76005
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). MR87j:73034
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 (1982). MR85k:35215
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).
Career information
PhDs.org Science, Math, and Engineering Career Resources
Some mathematical resources
Cornell:
Project Euclid Digital
Library Math Collection
Electronic Journal of Differential
Equations
Electronic Library of Mathematics
IMU - International Mathematical Union
Stackexchange: Math
Academia TeX Mathematica
mp_arc:
Mathematical Physics Archive
Trondheim: Conservation Laws PreprintServer
Portail Documentaire Mathematique
American Mathematical Society journals
Conformal Geometry and Dynamics
Electronic Research Announcements
SIAM journals
Oxford University Press
IMA Journal of Applied Mathematics
IMA Journal of Numerical Analysis
Proceedings of the Edinburgh Mathematical Society
The Quarterly Journal of Mathematics
The Quarterly Journal of Mechanics and Applied Mathematics
Other titles
American Journal of Mathematics
J. fur die reine und angewandte Mathematik (Crelle's Journal)
New York Journal of Mathematics
Pacific Journal of Mathematics
Regular and Chaotic Dynamics Home Page
JSTOR archives
Journal of the American Mathematical Society
Proceedings of the American Mathematical Society
SIAM Journal on Applied Mathematics
SIAM Journal on Numerical Analysis
Transactions of the American Mathematical Society
The Fields Institute for Research in Mathematical Sciences
In science 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.
Carl 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"