Displaying similar documents to “On the first mixed problem for a parabolic equation with right side in L l o c 2 ”

Determination of the unknown source term in a linear parabolic problem from the measured data at the final time

Müjdat Kaya (2014)

Applications of Mathematics

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The problem of determining the source term F ( x , t ) in the linear parabolic equation u t = ( k ( x ) u x ( x , t ) ) x + F ( x , t ) from the measured data at the final time u ( x , T ) = μ ( x ) is formulated. It is proved that the Fréchet derivative of the cost functional J ( F ) = ∥ μ T ( x ) - u ( x , T ) ∥ 0 2 can be formulated via the solution of the adjoint parabolic problem. Lipschitz continuity of the gradient is proved. An existence result for a quasi solution of the considered inverse problem is proved. A monotone iteration scheme is obtained based on the gradient method. Convergence...