## Unbounded solutions of the nonlinear heat-conduction equation with strong convection at infinity.(English. Russian original)Zbl 0924.76105

Comput. Math. Math. Phys. 36, No. 10, 1381-1391 (1996); translation from Zh. Vychisl. Mat. Mat. Fiz. 36, No. 10, 73-86 (1996).
Summary: We consider the equation of Newtonian polytropic flow through a porous medium with convective transfer. We prove the existence and uniqueness of a generalized solution of the Cauchy problem with an initial function which increases in a certain way to $$+\infty$$ and has an arbitrary increase as $$x\to-\infty$$. The behaviour of generalized solutions which increase to infinity as $$t\to\infty$$ is investigated.

### MSC:

 76S05 Flows in porous media; filtration; seepage 35K05 Heat equation 80A20 Heat and mass transfer, heat flow (MSC2010)