Seminar talk, 10 February 2021

Speaker: Alexey Samokhin

Title: On Monotonic Pattern in Periodic Boundary Solutions of Cylindrical and Spherical Kortweg-De Vries Burgers Equations

Abstract:
We studied, for the Kortweg-de Vries Burgers equations on cylindrical and spherical waves, the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary.

The regular profile at the vicinity of perturbation looks like a periodical chain of shock fronts with decreasing amplitudes. Further on, shock fronts become decaying smooth quasi periodic oscillations. After the oscillations cease, the wave develops as a monotonic convex wave, terminated by a head shock of a constant height and equal velocity. This velocity depends on integral characteristics of a boundary condition and on spatial dimensions.

The explicit asymptotic formulas for the monotonic part, the head shock and a median of the oscillating part are found.