6 documents found, page 1 of 1
Diffusion equations and different spatial fractional derivatives
Duarte, Alexandre F. B.; Pereira, Jessica de M. Gatti; Lenzi, Marcelo Kaminski; Gonçalves, Giane; Rossato, Roberto; Lenzi, Ervin KaminskiWe investigate for the diffusion equation the differences manifested by the solutions when three different types of spatial differential operators of noninteger (or fractional) order are considered for a limited and unlimited region. In all cases, we verify an anomalous spreading of the system, which can be connected to a rich class of anomalous diffusion processes.
Nonlinear diffusion equation, solutions and anomalous diffusion - DOI: 10.4025/...
Badini, Renata Ferreira Colli; Gonçalves, Giane; Lenzi, Marcelo Kaminski; Santos, Onélia Aparecida Andreo dos; Jorge, Luiz Mário de MatosThis work aimed to investigate a nonlinear diffusion equation by considering the presence of a time dependent diffusion coefficient, convective and absorbent terms. The nonlinear terms present in the diffusion equation are consequence of employing a nonlinear generalization of Darcy’s law or a nonlinear absorbent term, which may be related to a reaction diffusion process. Particularly, we will obtain new classe...
Modeling of integral reactor applied methane steam reforming - DOI: 10.4025/act...
Lenzi, Giane Gonçalves; Russo, Daniel; Lenzi, Ervin Kaminski; Santos, Onélia Aparecida Andreo dos; Jorge, Luiz Mário de MatosFrequently, the validation of applied mathematical models of industrial reactors dash into the difficulty of obtaining reliable experimental data. A way to overcome this limitation is the proper use and operation or a in bench scale, experimental setup from which experimental data can be obtained in controlled conditions. In this context, experiments were carried out in an integral reactor of steam reform, in d...
Nonlinear fractional diffusion equation: exact solutions - DOI: 10.4025/actasci...
Gonçalves, Giane; Lenzi, Marcelo Kaminski; Lenzi, Ervin Kaminski; Antonio, Fernando José; Schot, AlexandreWe devote this work to investigate the solutions of a generalized diffusion equation which contains spatial fractional derivatives and nonlinear terms. The presence of external forces and absorbent terms is also considered. The solutions found here can have a compact or long tail behavior. Particularly in the last case in the asymptotic limit, we relate these solutions to the Lévy or Tsallis distributions. In a...
Anomalous diffusion and fractional diffusion equations
Gonçalves, Giane; Lenzi, Marcelo Kaminski; Moraes, Luciana de Souza; Lenzi, Ervin Kaminski; Andrade, Marcelo Freitas deIn this work we investigate the anomalous diffusion equations, usually applied to describe the anomalous diffusion, which employ fractional derivatives for the time or the spatial variables. In particular, we obtain exact solutions by taking a generic initial condition into account and developing a perturbation theory to investigate complex situations. We also verify that the fractional derivatives, when applie...
Exact solutions for fractional diffusion equation: Green function approach - DO...
Gonçalves, Giane; Moraes, Luciana de Souza; Santos, Onélia Aparecida Andreo dos; Lenzi, Ervin KaminskiWe investigate the solutions for a fractional diffusion equation with radial symmetry, using the green function approach and taking the n-dimensional case into account. In our analysis, we consider a spatial time dependent diffusion coefficient and the presence of external forces. In particular, we discuss the results obtained by employing boundary condition defined on a finite interval and after, we extend the...