Välkommen till en föreläsning i seminarieserien i matematik.
Professor Adrian Muntean, Karlstads universitet
Reaction-diffusion systems with distributed microstructures: well-posedness and homogenization asymptotics
I will speak about multiscale modeling, analysis and approximation of a class of reaction-diffusion systems posed simultaneously on both macroscopic and microscopic space scales. The coupling between the scales is done via micro-macro transmission conditions. The PDE structure we wish to emphasize concerrns reaction-diffusion-flow problems through media with distributed microstructures double/dual porosity materials), reminding the work of G. I. Barenblatt on flows through fractured media. The talk will focus on an elementary derivation of the two-scale structure based on formal homogenization asymptotics. Then I will give a hint on how can one handle the weak solvability of the system and will point out a route to justify the homogenization asymptotics rigorously. A numerical example will illustrate how the weak solution "communicates" between micro and macro space scales. If time allows, I will outline as well a couple of our research questions connecting the modeling, mathematical analysis and simulation of interacting particles systems with the motion of social groups (crowd dynamics).
Seminariet arrangeras av institutionen för matematik. Se kommande och tidigare seminarier i serien.