Respected one, I want to know what the spherical means method is to solve a wave equation of two dimensions.
It is a method of solving the wave equation based on the observation that wave travels symmetrically in all directions. That observation leads to derivation of PDEs of average values over balls with fixed radius. Upon some (dimension-dependent) transformation, one can derive a PDE of the average value at a fixed center with radius and time as independent parameters. This PDE can be solved given the knowledge of the solution of the $1$-dimensional wave equation. The final solution can be obtained by transforming back.
I think this is a good read.