Irene Gamba
(Austin, Texas, USA)

Non-conservative models of multi-linear particle interactions

We look at extensions Kac N-particle model of pair interactions to an N-particle model which includes multi-particle interactions in Fourier/Laplace transformed space. Under molecular chaos assumption, one obtains a multi-linear integro-evolution equation that can be view as extensions of Boltzmann model dynamics of Maxwell type for conservative or dissipative interactions.

We shall study the evolution of the corresponding probability density solution. Under the assumption temporal invariance under scaling transformations of the phase space and contractive properties,
we obtain a full description of existence, uniqueness and long-time behavior to self-similar states, all from its spectral properties as well as the formation of power tails in their self similar state.

We also focus on a couple of new examples of multi-agent dynamics and information sharing and percolation models.