Domains of fractional powers of the heat-structure operator with viscoelastic damping: regularity and control-theoretic implications

摘要

We consider a heat-structure interaction model where the structure is subject to viscoelastic (strong) damping. The system displays high-order boundary coupling at the interface between the two media. If -A is the free dynamic operator, we characterize the domains of fractional powers D(A(theta)). Implications include optimal (maximal) regularity of the map: boundary control -> solution, where the control acts in the Dirichlet boundary conditions either at the external boundary of the heat domain, or else at the interface between the two domains. The optimal control theory and min-max game theory in Lasiecka and Triggiani (Encyclopedia of mathematics and its applications series. Cambridge University Press, Cambridge, 2000) then apply with the parameter gamma= 3 / 4 + is an element of.