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Well-posedness of a mathematical model for moisture transport appearing in concrete carbonation process. (English) Zbl 1282.35186
Summary: In a previous paper we have proposed a mathematical model for moisture transport in concrete carbonation process. The model consists of a diffusion equation for moisture and a parabolic equation which is a description of an approximation for a hysteresis operator indicating the relationship between the relative humidity and the degree of saturation. Also, on the problem with approximation of the hysteresis operator we showed the global existence of a solution and the uniqueness was proved in only one-dimensional space. Our aim of this paper is to give a complete proof of the existence of a solution without approximation.

35K51 Initial-boundary value problems for second-order parabolic systems
35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators
47J40 Equations with nonlinear hysteresis operators
35Q74 PDEs in connection with mechanics of deformable solids
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74N30 Problems involving hysteresis in solids