ASYMPTOTIC RESEARCH OF NONLINEAR-WAVE PROCESSES IN SATURATED POROUS-MEDIA

The problem of nonlinear wave dynamics of a fluid-saturated porous med ium is investigated. The mathematical model proposed is based on the c lassical Frenkel-Biot-Nikolaevskiy theory concerning elastic wave prop agation and includes mass, momentum, energy conservation laws, as well as rheological and thermodynamic relations. The model describes nonli near, dispersive, and dissipative medium. To solve the system of diffe rential equations, an asymptotic modified two-scales method is develop ed and a Cauchy problem for initial equations system is transformed to a Cauchy problem for nonlinear generalized Korteweg-de Vries-Burgers equation for modulated quick wave amplitudes and an inhomogeneous set of equations for slow background motion. Stationary solutions of the d erived evolutionary equation that have been constructed numerically re flect different regimes of elastic wave attenuation: diffusive, oscill ating, and soliton-like.