A Diffusion Equation with a Nonmonotone Constitutive Function.
Abstract
In this report we first review known (previously unpublished) a priori estimates for (P), and we then give a simpler construction for the existence of infinitely many solution of (P) for a piecewise linear phi as suggested by G. Strang. we then investigate further the qualitative behavior of solutions of (P). Motivated by known results in one space dimension for the steady state, non-elliptic problem, we study the analogous convexified problem associated with (P). Analytical and numerical considerations suggest that the unique solution of the convexified problem (which has a monotone, nondecreasing constitutive function) can be interpreted as an average of solutions of (P), whenever the data f'(.) reach the critical range.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1982
- Accession Number
- ADA124345
Entities
People
- John A. Nohel
- Klaus Hollig
Organizations
- University of Wisconsin–Madison