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| In this talk, we consider the system consisting of some nonlinear parabolic equation and an ordinary differential equation which describes a hysteresis operator. This problem is proposed as a mathematical model of moisture transport in concrete carbonation process, and we already proved the existence of a time global solution of our problem with an inhomogenious Dirichlet boundary condition and initial condition. The uniqueness of a solution is only obtained in one dimensional case, and is not be obtained in three dimensional case. The difficulties of the uniqueness of a solution in three dimensional case is a treatment of a nonlinear term in our parabolic type equation and a topology of a solution of the ordinary differential equation with a multivalued mappings. The aim of this talk is to prove the uniqueness of a solution of our problem in three dimensional case under the smooth boundary and initial data. |
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