Homogenization of integro-differential equation of Burgers type

Abstract:

Non-linear partial differential equation of Burgers type with integral term is considered. Its coefficients are rapidly oscillating functions. The equation describes wave propagation in stratified media with relaxation. Existence and uniqueness of solution is proved. Homogenized equation with constant coefficients is constructed. Convergence of exact solution to homogenized problem solution is proved.

Keywords: nonlinear equation; relaxation; energy estimates; Galerkin method; homogenization; asymptotic expansion

Document Type: Research article

DOI: 10.1080/00036810701697336

Affiliations: 1: LaMUSE EA 3989, University Jean Monnet, Saint Etienne, France 2: LaMUSE EA 3989, University Jean Monnet, Saint Etienne, France,Moscow State University M.V.Lomonosov, MechMath Department, Moscow, Russia