Faculty Jack Schaeffer, Professor
Ph.D., Indiana University
E-mail: js5m@andrew.cmu.edu
Office: Wean Hall 7113
Phone: 412-268-3561

Research:

My research concerns nonlinear partial differential equations, particularly hyperbolic equations. My recent work concerns kinetic models of plasma physics such as the Vlasov-Maxwell system. In these models the motion of a charge distribution is coupled to the evolution of the electromagnetic field. The existence of smooth solutions globally in time has been a major focus of mine, and numerical simulation has become another major focus more recently.

Selected Publications:

• 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).