Adrian Muntean: Reaction-diffusion systems with distributed microstructures

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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).


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