Reactive Processes in Random Media

Start: 09/06/2017 - 4:15pm
End  : 09/06/2017 - 5:15pm


Andrej Zlatos (UCSD)


We study propagation of reactive processes, such as forest fires or spreading of invasive species, in random heterogeneous environments and show that homogenization takes place under suitable hypotheses.  That is, on large space-time scales the effects of the small-scale heterogeneities average out, and the dynamics of solutions to the partial differential equations (PDEs) that model these processes become effectively homogeneous.  Interestingly, while the original PDEs are second-order (reaction-diffusion) equations, the "homogenized" PDEs that govern the large-scale dynamics are first-order (Hamilton-Jacobi) equations.  A key ingredient in this work is a new relationship between spreading speeds and front speeds for these models, as well as a new method to prove existence of these speeds.  

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