The radiative transfer equation: model and recent results

Did you ever wonder why the sky is blue or why in the shadow it is colder than under the sunlight? The radiative transfer equation is the kinetic equation which describes the interaction of matter with radiation. In this talk I will introduce the radiative heat transfer and the underlying model, as well as some recent results on the existence of solutions, asymptotic behavior, free boundary problems and inverse problems. Finally, future perspectives will be presented.