Mentrelli, Andrea; Pagnini, Gianni Random front propagation in fractional diffusive systems. (English) Zbl 1338.60110 Commun. Appl. Ind. Math. 6, No. 2, Article ID 504, 19 p. (2014). Summary: Modeling the propagation of interfaces is of interest in several fields of applied sciences, such as those involving chemical reactions where the reacting interface separates two different compounds. When the front propagation occurs in systems characterized by an underlying random motion, the front gets a random character and a tracking method for fronts with a random motion is desired. The level set method, which is a successful front tracking technique widely used for interfaces with deterministic motion, is here randomized assuming that the motion of the interface is characterized by a random diffusive process. In particular, here we consider the case of a motion governed by the time-fractional diffusion equation, leading to a probability density function for the interface particle displacement given by the M-Wright/Mainardi function. Some numerical results are shown and discussed. Cited in 2 Documents MSC: 60G22 Fractional processes, including fractional Brownian motion 60J60 Diffusion processes 60K37 Processes in random environments 35F21 Hamilton-Jacobi equations 65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs 65C99 Probabilistic methods, stochastic differential equations Keywords:random front propagation; time-fractional diffusion; level set method; M-Wright/Mainardi function PDFBibTeX XMLCite \textit{A. Mentrelli} and \textit{G. Pagnini}, Commun. Appl. Ind. Math. 6, No. 2, Article ID 504, 19 p. (2014; Zbl 1338.60110)