Integro-differential Burgers equation. Solvability and homogenization Original Research Article

We consider the integro-differential Burgers equation which appears in nonlinear acoustics. The integral term in the right-hand side describes the relaxation (memory) effects. The global existence and uniqueness of solution is proved. The smoothness of the solution is studied. In the case when the coefficients of the equation rapidly oscillate, we replace it by the homogenized equation with constant coefficients and prove the error estimates.