Research Contract N00014-68-A-0151 is engaged in the development of a computer information system in support of design, simulation and command/control. One aspect of the project is the development of general purpose computer programs for systems analysis. The present report is the analytical phase of a system identification (generalized mathematical modeling) package based on quasilinearization. A user-oriented computer software subsystem is available to aid in the application of the process described in this report and will be described in a subsequent user's manual. Additional information on the availability of the program and its relation to an integrated design and simulation system may be obtained from: Cullen College of Engineering, Project THEMIS, University of Houston, Houston, Texas 7 7 0 0 4. 0-ACKNOWLEDGEMENTS This paper is based upon the doctoral thesis *c. of the senior author. ABSTRACT A procedure f o r i d e n t i f i c a t i o n i n p a r t i a l d i f f e r e n t i a l equations i s described and i l l u s t r a t e d by t h e Laplace equation and t h e unsteady h e a t conduction equation. The procedure f o r s o l u t i o n involves t h e s u b s t i t u t i o n of d i f f e r e n c e o p e r a t o r s f o r t h e p a r t i a l d e r i v a t i v e s with r e s p e c t t o a l l but one of t h e independent v a r i a b l e s. The l i n e a r boundary value problem i s solved by s u p e r p o s i t i o n of p a r t i c u l a r s o l u t i o n s. For n o n l i n e a r boundary value problems which a r i s e from t h e o r i g i n a l form of t h e equation o r from t h e i d e n t i f i c a t i o n procedure, a Newton-Raphson-Kantorovich expansion i n f u n c t i o n space i s used t o reduce t h e s o l u t i o n t o an i t e r a t i v e procedure of solving l i n e a r boundary v a l u e problems. For t h e problems considered, t h i s procedure has proven t o be e f f e c t i v e and r e s u l t s i n a reasonable approximation t o t h e s o l u t i o n of t h e boundary value problem i n p a r t i a l d i f f e r e n t i a l equations. For t h e i d e n t i f i c a t i o n problem, it i s shown t h a t t h e constant parameters a r e i d e n t i f i e d t o t h e same accuracy as t h e supplementary data used i n t h e i d e n t i f i c a t i o n procedure.

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where s2 is a bounded domain in R"(n 2 3) with C2," boundary and a(x, s) satisfiesfor any S < mThe conditions (0.3) and (0.4) provide an a priori estimate, which can be used to prove existence (u E W2.p(Cl) for all p > n ) and uniqueness for the Dirichlet problem (0.1) and (0.2) via a topological fixed point theorem (see [ 11, Chapter 1 1 ).Therefore the Dirichlet to Neumann map is well defined, mapping W(2P-1)/PJ'(Ofl) into W(p-')'p,p(ds2).to the corresponding Dirichlet problems (0.1)-(0.2). We introduce the notation