Inverse problems in partial differential equations

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1968

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Abstract

A procedure for identification in partial differential equations is described and illustrated by the Laplace equation and the unsteady heat conduction equation. The procedure for solution involves the substitution of difference operators for the partial derivatives with respect to all but one of the independent variables. The linear boundary value problem is solved by superposition of particular solutions. For nonlinear boundary value problems which arise from the original form of the equation or from the identification procedure, a Newton-Raphson-Kantorovich expansion in function space is used to reduce the solution to an iterative procedure of solving linear boundary value problems. [...]

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