Large-time behavior of a two-scale semilinear reaction-diffusion system for concrete sulfatation

Fast-reaction asymptotics for a two-scale reaction-diffusion system

We investigate a reaction–diffusion process in a two-phase medium with microscopic length scale ε. The diffusion coefficients in the two phases are highly different (d1/D = ε2) and the reaction constant k is large. First, the homogenisation limit ε → 0 is taken, which leads to a two-scale model. Afterwards, we pass to the fast-reaction limit k →∞ and obtain a two-scale reaction-diffusion system...

Large-time behavior of solutions to a reaction-diffusion system with distributed microstructure

We study the large-time behavior of a class of reaction-diffusion systems with constant distributed microstructure arising when modeling diffusion and reaction in structured porous media. The main result of this Note is the following: As t→∞ the macroscopic concentration vanishes, while the microscopic concentrations reach constant concentration profiles independent of the shape of the microstr...

A two-scale reaction-diffusion system with micro-cell reaction concentrated on a free boundary

We discuss the fast-reaction limit of a two-scale reaction-diffusion model. We point out that if the reaction constant a explodes to infinity, then a two-scale PDEs system with free boundary at the micro cell is obtained. The aim of this note is to answer the question: Can the same two-scale free-boundary problem be obtained if we first pass to the fast-reaction limit a → ∞ and then take the ho...

A TWO-STAGE METHOD FOR DAMAGE DETECTION OF LARGE-SCALE STRUCTURES

A novel two-stage algorithm for detection of damages in large-scale structures under static loads is presented. The technique utilizes the vector of response change (VRC) and sensitivities of responses with respect to the elemental damage parameters (RSEs). It is shown that VRC approximately lies in the subspace spanned by RSEs corresponding to the damaged elements. The property is leveraged in...

Large scale reaction front dynamics in anisotropic reaction-diffusion systems