Andrew Acker

Andrew Acker, Professor

Partial Differential Equations; PhD, Boston University, 1972

Contact

Awards

Habilitation, University of Karlsruhe, January 1982.

PhD Students

Dr. Ruth Meyer, "Approximation of the Solutions of Free Boundary Problems for the Laplace Equation", PhD thesis, 1993
Dr. Ercan Kadakal, "On the Successive Approximations of Solutions to Some Elliptic Free Boundary Problems", PhD thesis, 1996

Research

Dr. Acker's primary research interest lie in the area of free-boundary problems for elliptic partial differential equations, with special emphasis on problems in fluid dynamics. His work in this area includes the Bernoulli problem, the multi-layer fluid problem, the Prandtl-Batchelor problem (vorticity localization in a potential flow), and the Tokomak machine (plasma localization in a magnetic field). Results have mostly involved existence of solutions, their uniqueness, their geometric properties, and their successive approximation. He has also published work on stability of feedback systems and the quenching problem for parabolic equations.

Selected Publications

  • (with W. Walter) The quenching problem for nonlinear partial differential equations. Ordinary and Partial Differential Equations, Dundee, 1976. Lecture Notes in Math., Vol. 564, 1-12. Springer Verlag, 1976.
  • Interior free boundary problems for the Laplace equation. Archive Rat'l. Mech Anal., Vol. 75 (1981), pp. 157-168.
  • On the qualitative theory of parametrized families of free boundaries. J. reine angev. Math., Vol. 393 (1989), pp. 134-167.
  • On the existence of convex classical solutions to multilayer free boundary problems with general nonlinear joining conditions. Trans. Amer. Math. Soc., Vol. 350 (1998), pp. 2981-3020.
  • On the existence of convex classical solutions to a generalized Prandtl-Batchelor free-boundary problem, Part I. J. Appl. Math. Phys., (ZAMP) Vol. 49 (1998), pp. 1-30.
  • On the existence of convex classical solutions to a generalized Prandtl-Batchelor free-boundary problem, Part II. J. Appl. Math. Phys., (ZAMP) Vol. 53 (2002), pp. 438-485.