A Source Term Inversion Problem for Degenerate Parabolic Equations
In reconstructing the degraded heat conduction equation by using terminal temperature observations,the inverse problem of spatially dependent heat sources is studied.The inverse problem is transformed into an optimization problem based on the optimal control framework,the necessary condition for the existence of the minimum value of the objective functional is proved.A method for constructing a second-order precision difference scheme is proposed,and the numerical solution of the inverse problem is obtained by the conjugate gradient method,which improved the convergence speed of the algorithm.The numerical experimental results indicate that the designed algorithm has high inversion efficiency and stability,and can achieve good results in reconstructing unknown heat sources.
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