Accession Number : AD0264427

Title :   THE DETERMINATION OF COEFFICIENTS IN PARABOLIC DIFFERENTIAL EQUATIONS BY MEASUREMENTS IN THE INTERIOR OF THE MEDIUM

Corporate Author : RICE UNIV HOUSTON TEX

Personal Author(s) : JONES,B. FRANK JR.

Report Date : JUL 1961

Pagination or Media Count : 1

Abstract : Unknown c efficients in a parabolic differential equation are determined by giving additional information about the solution of the differential equation. Consider the heat equation, du/dt equals a(t)(d(du/dx)), in either a bounded medium with zero boundary values or in an infinite rod. Here both a(t) and u(x,t) are unknown. If certain initial values for u(x,t) are prescribed and if u(x,t) is measured for all t and for some fixed initial x, then there is exactly one pair a(t) and u(x,t) satisfying the differential equation together with the boundary and initial conditions, and such that u(x,t) takes require values at fixed initial x.

Descriptors :   *PARTIAL DIFFERENTIAL EQUATIONS, INTEGRAL EQUATIONS, THEORY

Distribution Statement : APPROVED FOR PUBLIC RELEASE