Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes

The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, $u_t=J*u-u:=Lu$, in an exterior domain, $\Omega$, which excludes one or several holes, and with zero Dirichlet data on $\mathbb{R}^N\setminus\Omega$. When the space dimension is three or more this behavior is given by a multiple of the fundamental solution of the heat equation away from the holes. On the other hand, if the solution is scaled according to its decay factor, close to the holes it behaves like a function that is $L$-harmonic, $Lu=0$, in the exterior domain and vanishes in its complement. The height of such a function at infinity is determined through a matching procedure with the multiple of the fundamental solution of the heat equation representing the outer behavior. The inner and the outer behavior can be presented in a unified way through a suitable global approximation

Boundary fluxes for non-local diffusion

We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence, uniqueness and a comparison principle. Next, we study the behavior of solutions for some prescribed boundary data including blowing up ones. Finally, we look at a nonlinear flux boundary condition

Ligninolytic enzyme activities and colonization by Anthracophyllum discolor on lignocellulosic supports

FONDECYT Nº109067

A nonlocal inhomogeneous dispersal process

AbstractThis article in devoted to the study of the nonlocal dispersal equationut(x,t)=∫RJ(x−yg(y))u(y,t)g(y)dy−u(x,t)in R×[0,∞), and its stationary counterpart. We prove global existence for the initial value problem, and under suitable hypothesis on g and J, we prove that positive bounded stationary solutions exist. We also analyze the asymptotic behavior of the finite mass solutions as t→∞, showing that they converge locally to zero

Selection of white-rot fungi to formulate complex and coated pellets for Reactive Orange 165 decolourization

Six strains of white-rot fungi isolated from southern Chile were evaluated for their ergosterol/biomass correlation and ligninolytic potential in solid medium to formulate pellets for Reactive Orange 165 (RO165) decolourization. The fungus Anthracophyllum discolor was selected to formulate complex pellets (fungal mycelium, sawdust, and activated carbon), coated pellets (complex pellet + alginate) and simple pellets (fungal mycelium). The activity of ligninolytic enzymes (laccase, manganese peroxidase, manganese-independent peroxidase, and lignin peroxidase) was evaluated in both the complex and coated pellets in modified Kirk medium, and the morphology of the pellets was studied using scanning electron microscopy (SEM). Complex pellets of A. discolor showed a higher enzymatic production mainly MnP (38 U L-1 at day 15) compared to coated and simple pellets. Examinations using SEM showed that both pellets produced a black core that was entrapped by a layer of fungal mycelium. Decolourization of RO165 was demonstrated with all the pellets formulated. However, the highest and fastest decolourization was obtained with complex pellets (100% at day 8). Therefore, complex pellets of A. discolor can be used for the biological treatment of wastewater contaminated with RO165.This research was supported by a FONDECYT grant 1090678 and a Doctoral thesis fellowship CONICYT 24100149

Ligninolytic enzymes activities and SEM analysis of fungal inoculum of Anthracophyllum discolour

Fungal inocula are used for biotechnological applications especially in bioremediation process. They are formulated with a carrier, nutrient sources, binder, and lubricant to be encapsulated for a layer of fungal mycelium. The white-rot fungus Anthracophyllum discolor was studied for its ability to growth actively to form these inocula and to produce ligninolytic enzymes. In this study, fungal inocula were formulated on 3 different mixtures of lignocellulosic materials: F1, F2 and F3 and, two kind of fungal inocula were produced, coated and uncoated. The ligninolytic enzymes Laccase (Lac), Manganese Peroxidase (MnP), Manganese-independent Peroxidase (MiP) and Lignin Peroxidase (LiP) were measured during the experiments. The main enzymatic activity detected was Manganese Peroxidase for F1, F2 and, F3 tested and Laccase had the lowest activity. The amount of total ligninolytic enzyme activity was approximately 40% higher on uncoated than coated pellets, demonstrating the capacity of Anthracophy/lum discolor to growth and produce enzymes on this formulation. Uncoated pellet showed the highest MnP activity, after 15 days in average was 477,13 mmol/min/g being the pick of enzyme at the day 15 with 220,99 mmol/min/g. In contrast for coated pellets the MnP activity was 271,15 mmol/min/g. The UP was not detected on fungal inocula studied. Based on the results of ligninolytic enzymes, the fungal ability to growth and colonization on these pellet formulations showed by scanning electron microscopy (SEM), the pellet uncoated formulated with F1 lignocellulosic materials presents high potential to be used on bioremediation processes. These results will be presented and discussed