The Journal of the Australian Mathematical Society. Series B. Applied Mathematics

Research Article

Determination of a control parameter in a parabolic partial differential equation

J. R. Cannona1, Yanping Lina2 and Shingmin Wanga3

a1 Department of Mathematics, Lamar University, Beaumont, TX 77710.

a2 Department of Applied Mathematics, University of Waterloo, Waterloo, Canada N2L 3G1.

a3 Division of Mathematics and Computer Science, Northeast Missouri State University, Kirksville, MO 63501.

Abstract

The authors consider in this paper the inverse problem of finding a pair of functions (u, p) such that

S0334270000006962_eqnU1

where F, f, E, s, αi, βi, γi, gi, i = 1, 2, are given functions.

The existence and uniqueness of a smooth global solution pair (u, p) which depends continuously upon the data are demonstrated under certain assumptions on the data.

(Received November 25 1988)

(Revised June 22 1989)