This talk is devoted to the influence of stochastic perturbations on the long time behavior of nonlocal evolution equations, such as the bidomain model of heart tissue, and the aggregation-diffusion equation (Keller-Segel model). The nonlocal character of these equations can be present either in the differential operator (bidomain) or in the reaction term (Keller-Segel). Using the fundamental concepts in the area of stochastic analysis, semigroup theory and PDEs, in my talk, I will address the effects of noise on the existence and regularity of global vs. local solutions, various types of blowup behavior (Keller-Segel), as well as the existence and properties of invariant measures (for the bidomain model), which is the key step in establishing the qualitative behavior of the underlying physical system.

The speaker will present in person.