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Keywords:
uncertain data; optimal design approach; parabolic obstacle problems; penalization method; Fourier problem
uncertain data; optimal design approach; parabolic obstacle problems; penalization method; Fourier problem
Summary:
A class of parabolic initial-boundary value problems is considered, where admissible coefficients are given in certain intervals. We are looking for maximal values of the solution with respect to the set of admissible coefficients. We give the abstract general scheme, proposing how to solve such problems with uncertain data. We formulate a general maximization problem and prove its solvability, provided all fundamental assumptions are fulfilled. We apply the theory to certain Fourier obstacle type maximization problem.
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