Mariia Burlutskaia

On a Resolvent Approach in a Mixed Problem for the Wave Equation on a Graph

abstract:
We study a mixed problem for the wave equation with integrable potential on the simplest geometric graph consisting of two ring edges that touch at a point. We use a new resolvent approach in the Fourier method. We do not use refined asymptotic formulas for the eigenvalues and any information on the eigenfunctions.

Mathematics Subject Classification: 34B45, 35L05

Key words and phrases: Wave equation, geometric graph, Fourier method, resolvent approach