On initial-boundary value problem for the Burgers equation in nonlinearly degenerating domain
Jenaliyev M.T. Yergaliyev M.G.
2024Taylor and Francis Ltd.
Applicable Analysis
2024#103Issue 112003 - 2014 pp.
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.
Burgers equation , degenerating domain , Galerkin method , periodic boundary conditions
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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics, al-Farabi KazNU, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling
Department of Mathematics
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