Report to the Office of Naval Research for Contract N00014-89-J-1108 (Texas A&M University)
Abstract
This research concerns undetermined coefficient problems in partial differential equations, in particular those problems where the unknown coefficients depend only on the dependent variables. The problems modeled by these equations are related to the determination of unknown physical laws or relationships. The nonlinear terms which we seek to recover in our model problems correspond to material properties that have physical significance; temperature dependent specific heats, conductivities, reaction terms, to name a few. Examples of such problems are - the determination of an unknown reaction term f(dot) in u sub t - u sub xx = f(u), or the conductivity k(dot) in the equation Del dot k(u) Del u = 0. We seek to determine these functions by giving only overposed boundary data. This type of problem is distinct from those that involve media with unknown inhomogeneities; that is, the differential equations contain an unknown coefficient that depends on the independent spatial variable. In a given physical problem both situations may occur, that is, the unknowns have both spatial as well temperature dependence. This is a considerably more difficult problem and has received little attention in its full generality, instead both the limiting cases of dependence on a single one of these variables have and has received the vast majority of the research efforts. For those cases where the media is isotropic, the assumption that the unknowns depend only on the independent variable may be a very reasonable one. (jhd)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 31, 1989
- Accession Number
- ADA217169
Entities
People
- Michael Pilant
- William Rundell
Organizations
- Texas A&M University