Boundary Observability in the Quasi-Static Thermoelastic Contact Problem
نویسندگان
چکیده
Abstract We study the observability properties of a nonlinear parabolic system that models the temperature evolution of a thermoelastic rod that may come into contact with a rigid obstacle. Basically the system dynamics are described by a one-dimensional nonlocal partial differential equation of parabolic type with a nonlinear and nonlocal boundary condition. For a specified nonlocal observation operator, we show the system to be observable and get the estimates for the boundary temperature and the current state of the system. The technique of deriving the boundary estimate is essentially based on using Carleman-type estimates. Finally, for sufficiently smooth solutions, we show that the observability result is equivalent to the boundary observability of the system.
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