The problem of determining the initial condition in parabolic equations from boundary observations is studied. It is reformulated as a variational problem and then a formula for the gradient of the functional to be minimized is derived via an adjoint problem. The variational problem is discretized by finite difference splitting methods and solved by the conjugate gradient method. Some numerical examples are presented to show the efficiency of the method. Also as a by-product of the variational method, we propose a numerical scheme for numerically estimating singular values of the solution operator in the inverse problem.
Funding source: Vietnam National Foundation for Science and Technology Development (NAFOSTED)
Award Identifier / Grant number: 101.02-2014.54
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