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We propose a method for computing bounds on output functionals of a class oftime-dependent PDEs. To this end, we introduce barrier functionals for PDEsystems. By defining appropriate unsafe sets and optimization problems, weformulate an output functional bound estimation approach based on barrierfunctionals. In the case of polynomial data, sum of squares (SOS) programmingis used to construct the barrier functionals and thus to compute bounds on theoutput functionals via semidefinite programs (SDPs). An example is given toillustrate the results.

Barrier Functionals for Output Functional Estimation of PDEs