On the construction of singular solutions for kinetic equations
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Mon, 26/10/2009 17:00 |
Juan Velasquez (Universidad Complutense Madrid) |
Partial Differential Equations Seminar  |
Gibson 1st Floor SR |
| 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. | |||