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T. Levajković:
"Stochastic parabolic equations with singularities";
Talk: 9th Austrian Stochastics Days (ASD 2021), Leoben; 2021-09-09 - 2021-09-10.

This talk is devoted to the study of stochastic parabolic evolution problems where the coefficients, initial and boundary conditions might be highly singular, i.e., generalized stochastic processes. In the analysis of these evolution problems, we combine the polynomial chaos expansion (PCE) method with the concept of very weak solutions. The PCE method is a spectral method based on the tensor product of deterministic orthogonal polynomials as a basis in the space of square integrable stochastic processes. The main idea of the very weak solution concept is to model irregular objects in equations by approximating nets of regular functions with moderate asymptotic. The notion of a stochastic very weak solution is introduced and the existence of a corresponding stochastic initial value problem is proved. The questions on the uniqueness of the stochastic very weak solution as well as its consistency to the stochastic weak solution are discussed. The results are obtained in collaboration with Snezana Gordic and Ljubica Oparnica.