Department of Mathematical Sciences
Carnegie Mellon University
5000 Forbes Avenue
Pittsburgh, PA 15213
Ph.D., Indiana University
My research is in the general area of partial differential equations. Most of my work has concerned kinetic models of plasma, although highly similar models are use to describe the evolution of a galaxy. In these models the Vlasov equation is used to describe the state of the particles and the Vlasov equation is coupled to another equation which describes the field under which the particles move; this is usually Poisson's equation or Maxwell's equations.
Much of my work has concerned the global existence in time of smooth solutions to such systems, but asymptotic behavior is also of interest. Some work has also been done on numerical methods and convergence results for these problems. The study of steady (in time) solutions has been of interest recently.
Glassey, R. and Schaeffer, J., "On Global Symmetric Solutions to the Relativistic Vlasov-Poisson Equation in Three Space Dimensions", Math. Meth. Appl. Sci. 24, 143–157 (2001).
Schaeffer, J., "A Class of Counterexamples to Jeans' Theorem for the Vlasov-Einstein System", Commun. Math. Phys. 204, 313–327 (1999).
Schaeffer, J., "Convergence of a difference scheme for the Vlasov-Poisson-Fokker-Planck System in one dimension", SIAM J. Numer. Anal., Vol. 35, No. 3, 1149–1175 (1998).
Glassey, R. and Schaeffer, J., "The 'Two and One-Half Dimensional' Relativistic Vlasov Maxwell System", Commun. Math. Phys. 185, 257–284, (1997).
Rein, G., Rendall, A., and Schaeffer, J., "A Regularity Theorem for the Spherically Symmetric Vlasov-Einstein System," Commun. Math. Phys. 168, 467–478 (1995).
Schaeffer, J., "Global Existence of Smooth Solutions to the Vlasov-Poisson System in Three Dimensions", Commun. PDE 16(8&9), 1313–1335 (1991).