On initial-boundary value problem for the Burgers equation in nonlinearly degenerating domain

In this paper, we study the solvability of one initial-boundary value problem for the Burgers equation with periodic boundary conditions in a nonlinearly degenerating domain. In this paper, we found an orthonormal basis for domains with time-varying boundaries. On this basis, we use the Faedo-Galerkin method to prove theorems about the unique solvability of the problem under consideration. We also present some numerical results in the form of graphs of solutions to the problem under study for various initial data.

Automated summary

This paper studies the solvability of one initial-boundary value problem for the Burgers equation with periodic boundary conditions in a nonlinearly degenerating domain. An orthonormal basis for domains with time-varying boundaries is found, and the Faedo-Galerkin method is used to prove theorems about the unique solvability of the problem. Additionally, some numerical results in the form of graphs of solutions for various initial data are presented.