Accession Number : ADA136325

Title :   A Singular Free Boundary Problem.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Hollig,K ; Nohel,John A

PDF Url : ADA136325

Report Date : Oct 1983

Pagination or Media Count : 17

Abstract : The Cauchy problem is similar to the well-known one phase Stefan problem (inone space dimension). In the latter one would assume g(x) = -1 for x 0, as well as g(x) 0 for x 0, so that g would have a jump discontinuity at x = 0. Our assumptions on the initial data g yield a different behavior of the solution v and of the resulting free boundary. Indeed, the free boundary is not (infinitely) differentiable at t = 0, contrary to the situation for the classical Stefan problem. This problem also serves as a prototype of nonlinear parabolic problems which arise as monotone convexifications of nonlinear diffusion equations with nonmonotone constitutive functions phi. That analysis shows the existence of infinitely many solutions v of the nonmonotone problem each having v bounded, but oscillating more and more rapidly as t infinity 0(+). Thus each solution v exhibits phase changes. Numerical experiments further suggest the conjecture that the physically correct solution of the nonmonotone problem is the one which for t 0 sufficiently large approaches the unique solution of the appropriately related convexified monotone problem. This paper is another step towards the understanding of this intriguing phenomenon.

Descriptors :   *Cauchy problem, *Boundary value problems, Boundaries, Numerical methods and procedures, Operators(Mathematics), Prototypes, Diffusion, Nonlinear algebraic equations

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE