On the construction of singular solutions for kinetic equations

In this talk I will present the rigorous construction of

singular solutions for two kinetic models, namely, the Uehling-Uhlenbeck

equation (also known as the quantum Boltzmann equation), and a class of

homogeneous coagulation equations. The solutions obtained behave as

power laws in some regions of the space of variables characterizing the

particles. These solutions can be interpreted as describing particle

fluxes towards or some regions from this space of variables.

The construction of the solutions is made by means of a perturbative

argument with respect to the linear problem. A key point in this

construction is the analysis of the fundamental solution of a linearized

problem that can be made by means of Wiener-Hopf transformation methods.