Identification of the Right-Hand Side of an Equation with a Fractional Power of an Elliptic Operator
An inverse problem of identifying the right-hand side of an equation with a fractional power of an elliptic operator by the solution is considered. The direct problem is solved via solving a Cauchy problem for a pseudo-parabolic equation. The problem of identifying the right-hand side is reduced to a retrospective problem for this pseudo-parabolic equation. An iterative method is employed to adjust the initial condition. The results of numerical experiments for a 2D inverse problem are presented.
KeywordsFractional power of an elliptic operator Identification of the right-hand side Retrospective inverse problem Iterative method for solving an ill-posed problem
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