A general method for solving the Dirichlet problem for the Burgers equation with a moving boundary is introduced. The method reduces the initial value problem to a linear integral equation of Volterra type with mildly singular kernel, which admits a unique solution under rather general assumptions. Two explicit cases are considered: a boundary moving with constant velocity and a rapidly oscillating boundary.
On the Burgers equation with mouving boundary
DE LILLO, Silvana;
2001
Abstract
A general method for solving the Dirichlet problem for the Burgers equation with a moving boundary is introduced. The method reduces the initial value problem to a linear integral equation of Volterra type with mildly singular kernel, which admits a unique solution under rather general assumptions. Two explicit cases are considered: a boundary moving with constant velocity and a rapidly oscillating boundary. File in questo prodotto:
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