ИСТИНА

Asymptotic solutions of a wave equation degenerating on the boundary of the domain (where the wave propagation velocity vanishes on the boundary as the square root of the distance from the boundary) can be represented with the use of a modified canonical operator on an invariant Lagrangian submanifold of the nonstandard phase space constructed by the authors earlier. In the talk, we present simple expressions in a neighborhood of the boundary for the functions represented by the modified canonical operator and in particular for the solution of the Cauchy problem for the degenerating wave equation with initial data localized near an interior point of the domain. The research described in the talk was supported by the Russian Science Foundation within the framework of project no. 16-11-10282.