Well-posedness of a mathematical model for moisture transport appearing in concrete carbonation process.

*(English)*Zbl 1282.35186Summary: 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.

##### MSC:

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 |