{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/54233"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/54233","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Approximation and control of a thermoviscoelastic system","abstract":"In this paper consider the problem of controlling a thermoviscoelastic system. We present a semigroup setting for this system, and prove the well-posedness by applying a general theorem which is given in this paper. We also study the stability of the system. We give a finite element/averaging scheme to approximate the linear quadratic regulator problem governed by the system. We prove that yields faster convergence. We give a proof of convergence of the simulation problem for singular kernels and of the control problem for L2 kernels. 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