Concentration Phenomena of a Semilinear Elliptic Equation with Large Advection in an Ecological Model

We consider a reaction-diffusion-advection equation arising from a biological model of migrating species. The qualitative properties of the globally attracting solution are studied and in some cases the limiting profile is determined. In particular, a conjecture of Cantrell, Cosner and Lou on concentration phenomena is resolved under mild conditions. Applications to a related parabolic competition system is also discussed

Selected topics on reaction-diffusion-advection models from spatial ecology

We discuss the effects of movement and spatial heterogeneity on population dynamics via reaction-diffusion-advection models, focusing on the persistence, competition, and evolution of organisms in spatially heterogeneous environments. Topics include Lokta-Volterra competition models, river models, evolution of biased movement, phytoplankton growth, and spatial spread of epidemic disease. Open problems and conjectures are presented

Biocompatibility of degradable biomaterials:a study on the factors determining the inflammatory response against degradable polymers

The study reported in this thesis was undertaken to obtain more insight in the role of various factors determining the outcome of the interaction between biodegradable polymers and the host in which they are implanted. In the end, the outcome of this interaction determines the success or failure of the implant. Up till now, bioresorbable polymers, such as poly(L-lactide) and poly(g1ycolide) are mostly applied in suture material. However, much research is conducted for other clinical applications. E.g. artificial skin, meniscus prosthesis, abdominal wall prosthesis, nerve guides, bone plates for repairing fractures, small calibre vascular prosthesis, parodontal filters and drug delivery systems. There are many reasons for choosing a bioresorbable material. However, most of them can ultimately be derived from the adage of causing minimal damage to the host. Thus, no foreign material must be left in the host when a biomaterial has performed its function. This goes for drug delivery systems, as well as for those applications in which the function(s) of an organ or tissue is temporarily replaced by a biomaterial or a device made from biomaterials. Only a few of the vast array of polymers applied nowadays are bioresorbable and thus biodegradable

Invasion of open space by two competitors: spreading properties of monostable two-species competition--diffusion systems

International audienceThis paper is concerned with some spreading properties of monostable Lotka–Volterra two-species competition–diffusion systems when the initial values are null or exponentially decaying in a right half-line. Thanks to a careful construction of super-solutions and sub-solutions, we improve previously known results and settle open questions. In particular, we show that if the weaker competitor is also the faster one, then it is able to evade the stronger and slower competitor by invading first into unoccupied territories. The pair of speeds depends on the initial values. If these are null in a right half-line, then the first speed is the KPP speed of the fastest competitor and the second speed is given by an exact formula describing the possibility of non-local pulling. Furthermore, the unbounded set of pairs of speeds achievable with exponentially decaying initial values is characterized, up to a negligible set

Invasion of open space by two competitors: spreading properties of monostable two-species competition--diffusion systems

This paper is concerned with some spreading properties of monostable Lotka--Volterra two-species competition--diffusion systems when the initial values are null or exponentially decaying in a right half-line. Thanks to a careful construction of super-solutions and sub-solutions, we improve previously known results and settle open questions. In particular, we show that if the weaker competitor is also the faster one, then it is able to evade the stronger and slower competitor by invading first into unoccupied territories. The pair of speeds depends on the initial values. If these are null in a right half-line, then the first speed is the KPP speed of the fastest competitor and the second speed is given by an exact formula describing the possibility of non-local pulling. Furthermore, the unbounded set of pairs of speeds achievable with exponentially decaying initial values is characterized, up to a negligible set