Abstract
arises in simulating various processes in mechanics of continuous medium. Among them there are the process of heat (mass) transfer in mediums with thermal conductivity coefficient (diffusion) which powerwise depends on the temperature (concentration), and the process of filtering of polytropic gas into porous medium. In the last case (1.1) is called the Leibenson equation, and for m = 1 the Boussinesq equation. The same equation arises in dynamics of ground water. We shall consider (1.1) on the semiaxis x > 0 with the initial and boundary conditions u(x, 0) = cx (x > 0), u(0, t) = 0 (t > 0). (1.2)
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