(Invited Minisymposium)
10:45 AM-12:45 PM
Room: Atlanta 3
Degenerate elliptic equations arise in a number of continuum problems. Perhaps the best known is the porous medium equation, representing flow in a medium whose diffusivity depends on saturations. The medium may be isotropic or anisotropic; in either case, free boundary problems occur. Recent work on self-similar solutions of multidimensional conservation laws provides another source of such problems: the degeneracy is typically anisotropic, and mathematical results are just now being developed. The speakers in this minisymposium will discuss proved existence of solutions that change sign for a quasilinear model problem, positive solutions to an anisotropic problem, results on conservation law models and their application to weak shock reflection and the von Neumann paradox, and regularity results for a linear anisotropically degenerate equation.
Organizer: Barbara L. Keyfitz
University of Houston
LMH, 1/19/99, MMD, 1/26/99