The purpose of this project is to study the theory of well-posedness for the Cauchy problem of the fractional radiative transfer equation for general data and also study the stability/asymptotic behavior of solutions for such partial differential equations (EDPs) of order $s\in(0,1)$. We discuss equations that serve as model for physical phenomena associated to wave propagation of high-frequency or "long-range" waves. Moreover, linked to those models, we also consider 1D non-local models with singular velocities and fractional dissipations, which can provide insights for models in higher dimensions. We intend to develop methods and results for our target-set of problems that can also be extended to other classes of nonlocal PDEs.
News published in Agência FAPESP Newsletter about the scholarship: