Weakly differentiable functions
Weakly differentiable functions
Homogenizing the acoustic properties of the seabed: part I
Nonlinear Analysis: Theory, Methods & Applications - Lakshmikantham's Legacy: A tribute on his 75th birthday
Homogenizing the time-harmonic acoustics of bone: The monophasic case
Mathematical and Computer Modelling: An International Journal
Modelling of film casting manufacturing process longitudinal and transverse stretching
Mathematical and Computer Modelling: An International Journal
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We study acoustic wave propagation in a two-phase medium in which the solid phase is a linear elastic material, and the fluid phase is assumed to be a compressible Newtonian barotropic fluid. Assuming that properties of the medium change rapidly on the small scale @e, we analyze the microscopic nonlinear Navier-Stokes equations and show that they can be linearized when @e tends to zero. Using a variant of Tartar's method of oscillating test functions, we derive effective acoustic equations which turn out to be viscoelastic. In order to treat disordered materials occurring in nature, we develop a new approach to describing geometry of a nonperiodic medium with length scale separation. Our approach is not based on probabilistic considerations. Instead, we postulate that certain inequalities hold uniformly on the microscale.