Critical times in single-layer reaction diffusion

Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: Criteria for successful colonization

“…While many reaction-diffusion models are inherently nonlinear, there is a real practical value in the use of linear models, since linear PDE models are often used to approximate the solution of related nonlinear PDE models[27]. For example, Hickson et al [28] analyses the critical timescale of a nonlinear reaction-diffusion process by arguing that the nonlinear PDE model can be approximated by a linear PDE model. Similarly, Swanson [29] provides key insight into the motion of a moving front of cells by studying an exact solution of a linear PDE model.…”

Finite difference schemes for multilayer diffusion

“…(see [18,21,22,[29][30][31]). This question is of interest in a variety of fields (see for example [32,33]).…”

Diffusion Across Semi-permeable Barriers: Spectral Properties, Efficient Computation, and Applications

“…More precisely, one definition of the critical time is the time at which the average temperature over the sample is equal to some fraction α < 1 of the average steady-state temperature over the sample. Other definitions and a thorough comparison of these definitions are detailed in [46,47]. This time is essentially given by the study of the first nonzero eigenvalue of the diffusion operator, for which we are able to obtain estimates with respect to the geometrical parameters of the medium (such as Eq.…”