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Partial exact controllability for inhomogeneous multidimensional thermoelastic diffusion problem

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  • The problem of stabilization and controllability for inhomogeneous multidimensional thermoelastic diffusion problem is considered for anisotropic material. By introducing a nonlinear feedback function on part of the boundary of the material, which is clamped along the rest of its boundary, we prove that the energy of the system decays to zero exponentially or polynomially. Both rates of decay are determined explicitly by the physical parameters. Via Russell's ``Controllability via Stabilizability" principle, we prove that the considered system is partially controllable by a boundary function determined explicitly.
    Mathematics Subject Classification: Primary: 35B37; Secondary: 35B35.

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