We study the properties of space localization of weak solutions of the equation

which appears in the mathematical description of filtration of an ideal barotropic gas in a porous medium. The functions and are assumed to satisfy the nonstandard growth conditions: , , , , with some positive constants and measurable bounded functions , , . It is shown that if , , and , meet certain regularity requirements, then every weak solution possesses the property of finite speed of propagation of disturbances from the initial data. In the case that in a ball and in , the solutions display the waiting time property: if with a positive exponent , depending on and , and a sufficiently small , then there exists such that in .