Algebras of generalized functions in linear and nonlinear PDEs

Durata: 50 min. Abstract: The talk addresses linear and nonlinear partial differential containing strong singularities in the data or coefficients. We focus on situations formally involving products of distributions. After a survey on multiplication of distributions in applications, algebras of generalized functions are introduced, in which these type of problems can be solved. We demonstrate applications of the theory to semilinear wave equations with distribution data and to stochastic wave equations. Emphasis is put on the qualitative description of the properties of the generalized solution.