
Accession Number : ADA136325
Title : A Singular Free Boundary Problem.
Descriptive Note : Technical summary rept.,
Corporate Author : WISCONSIN UNIVMADISON 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 wellknown 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