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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)
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