Search

The goal of this paper is to provide analytical assessments to a fluid flowing in a porous medium with a non-linear diffusion linked to a degenerate diffusivity. The viscosity term is formulated with an Eyring-Powell law, together with a non-homogeneous diffusion typical of porous medium equations (as known in the theory of partial differential equations). Further, the equation is supplemented with an absorptive reaction term of Darcy-Forchheimer, commonly used to model flows in porous medium. The work starts by analyzing regularity, existence and uniqueness of solutions. Afterwards, the problem is transformed to study travelling wave kind of solutions. An asymptotic expansion is considered with a convergence criteria based on the geometric perturbation theory. Supported by this theory, there exists an exponential decaying rate in the travelling wave profile. Such exponential behaviour is validated with a numerical assessment. This is not a trivial result given the degenerate diffusivity induced by the non-linear diffusion of porous medium type and suggests the existence of regularity that can serve as a baseline to construct numerical or energetic approaches. [ABSTRACT FROM AUTHOR]

The goal of this study is to provide an analysis of a Fisher-KPP non-linear reaction problem with a higher-order diffusion and a non-linear advection. We study the existence and uniqueness of solutions together with asymptotic solutions and positivity conditions. We show the existence of instabilities based on a shooting method approach. Afterwards, we study the existence and uniqueness of solutions as an abstract evolution of a bounded continuous single parametric (t) semigroup. Asymptotic solutions based on a Hamilton–Jacobi equation are then analyzed. Finally, the conditions required to ensure a comparison principle are explored supported by the existence of a positive maximal kernel. [ABSTRACT FROM AUTHOR]

The goal of this study is to provide analytical and numerical assessments to a fluid flow based on an Eyring–Powell viscosity term and a Darcy–Forchheimer law in a porous media. The analysis provides results about regularity, existence and uniqueness of solutions. Travelling wave solutions are explored, supported by the Geometric Perturbation Theory to build profiles in the proximity of the equation critical points. Finally, a numerical routine is provided as a baseline for the validity of the analytical approach presented for low Reynolds numbers typical in a porous medium. [ABSTRACT FROM AUTHOR]

This work provides an analytical approach to characterize and determine solutions to a porous medium system of equations with views in applications to invasive-invaded biological dynamics. Firstly, the existence and uniqueness of solutions are proved. Afterwards, profiles of solutions are obtained making use of the self-similar structure that permits showing the existence of a diffusive front. The solutions are then studied within the Travelling Waves (TW) domain showing the existence of potential and exponential profiles in the stable connection that converges to the stationary solutions in which the invasive species predominates. The TW profiles are shown to exist based on the geometry perturbation theory together with an analytical-topological argument in the phase plane. The finding of an exponential decaying rate (related with the advection and diffusion parameters) in the invaded species TW is not trivial in the nonlinear diffusion case and reflects the existence of a TW trajectory governed by the invaded species runaway (in the direction of the advection) and the diffusion (acting in a finite speed front or support). [ABSTRACT FROM AUTHOR]

Copyright of Revista de Investigación Desarrollo e Innovación is the property of Universidad Pedagogica y Tecnologica de Colombia and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract  The August 1991 eruptions of Hudson volcano produced ~2.7 km3 (dense rock equivalent, DRE) of basaltic to trachyandesitic pyroclastic deposits, making it one of the largest historical eruptions in South America. Phase 1 of the eruption (P1, April 8) involved both lava flows and a phreatomagmatic eruption from a fissure located in the NW corner of the caldera. The paroxysmal phase (P2) began several days later (April 12) with a Plinian-style eruption from a different vent 4 km to the south-southeast. Tephra from the 1991 eruption ranges in composition from basalt (phase 1) to trachyandesite (phase 2), with a distinct gap between the two erupted phases from 54–60 wt% SiO2. A trend of decreasing SiO2 is evident from the earliest part of the phase 2 eruption (unit A, 63–65 wt% SiO2) to the end (unit D, 60–63 wt% SiO2). Melt inclusion data and textures suggest that mixing occurred in magmas from both eruptive phases. The basaltic and trachyandesitic magmas can be genetically related through both magma mixing and fractional crystallization processes. A combination of observed phase assemblages, inferred water content, crystallinity, and geothermometry estimates suggest pre-eruptive storage of the phase 2 trachyandesite at pressures between ~50–100 megapascal (MPa) at 972 ± 26°C under water-saturated conditions (log fO2 –10.33 (±0.2)). It is proposed that rising P1 basaltic magma intersected the lower part of the P2 magma storage region between 2 and 3 km depth. Subsequent mixing between the two magmas preferentially hybridized the lower part of the chamber. Basaltic magma continued advancing towards the surface as a dyke to eventually be erupted in the northwestern part of the Hudson caldera. The presence of tachylite in the P1 products suggests that some of the magma was stalled close to the surface ( [ABSTRACT FROM AUTHOR]