Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry’s law and time-dependent Dirichlet data

Abstract

We study the large-time behavior of the free boundary position capturing the one-dimensional motion of the carbonation reaction front in concrete-based materials. We extend here our rigorous justification of the √ t-behavior of reaction penetration depths by including non-linear effects due to deviations from the classical Henry's law and time-dependent Dirichlet data.

Convergence of a finite volume scheme for a parabolic system with a free boundary modeling concrete carbonation

“…As we will see later, the positive part is not necessary in the definition of ψ due to the nonnegativity of u. We note that it is also possible to consider a nonlinear source term f , corresponding to a nonlinear Henry's law as in [4]. However, in this paper we focus on the numerical analysis of a finite volume scheme for (1.1) in the linear case: p = 1 and with a linear f .…”

Numerical approximation of a concrete carbonation model: Study of the ‐law of propagation

“…As in the theoretical analysis, we suppose that the following assumptions are satisfied: ψ : ℝ → ℝ represents the kinetics of the reaction and is defined by ψ ( x ) = αx p with α > 0 and p ≥ 1, f : ℝ 2 → ℝ is given by the Henry's law and is defined by f ( u , v ) = β ( γv − u ) with β and γ two positive constants, g and r belong to H 1 (0, T ), u 0 and v 0 belong to L ∞ ([0, s 0 ]), the diffusive coefficients κ u and κ v are two positive constants, s 0 > 0, there exist g * and r * two positive constants with g * = γr * such that In , Aiki and Muntean show that the penetration depth s follows a ‐law of propagation for constant Dirichlet boundary conditions. In this case, they prove the existence of two positive constants c and C independent of t such that They extend their result to the case of time dependent Dirichlet boundary conditions in . We notice that there exists a wide literature in the continuous setting on the long time behavior of the free interface for Stefan like problem, see for instance and references therein.…”

“…They extend their result to the case of time dependent Dirichlet boundary conditions in [6]. We notice that there exists a wide literature in the continuous setting on the long time behavior of the free interface for Stefan like problem, see for instance [7][8][9][10] and references therein.…”

Continuous bodies with thermodynamically active singular sharp interfaces

“…Concerning mathematical free-boundary problems arising from singular interfaces, there are some results for a spatially onedimensional setting. We refer to [44,45] for application to solid mechanics and, for an application to moving reaction fronts in concrete, to [46][47][48]. Moreover, further challenges consist of developing suitable numerical algorithms and performing simulations in order to deal with applications.…”

“…In [8,9] non-homogeneous jump conditions at singular interfaces are considered. For an application to moving carbonation fronts in concrete we refer to [46][47][48]. As we will see in Section 4, in an idealized case, the loss of material can be dealt with, using only interfacial supplies.…”