Georgia Institute of Technology College of Sciences

The Guderley problem describes the behavior of a strong self-similar shock wave propagating radially in an ideal gas. A spherical shock converges radially inwards to the spatial origin, strengthening as it collapses. At the collapse point, the shock's strength becomes infinite, leading to the formation of a new outgoing shock wave of finite strength, which then propagates outwards to infinity. 

In this talk, I will present recent work on the rigorous construction of the self-similar converging and diverging shock solutions for $\gamma \in (1,3]$. These solutions are analytic away from the shock interfaces and the blow-up point. The proof relies on continuity arguments, nonlinear invariances, and barrier functions.