ABSTRACT
We consider the Cauchy problem for the porous medium equation with nonlinear convection. The emphasis m on the existence and uniqueness of nonnegative solutions in a classes of growing at an infinity functions. The convection term in the equation introduces an asymmetry, a different conditions at a minus and plus infinity for the initial data are needed. A behaviour of growing solutions for large time is studied too. A constructed examples show a certain exactness of the obtaining results.
