Large time behaviour in convection-diffusion equations. (English) Zbl 0870.35054

Carpio, A.

Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 23, No. 3, 551-574 (1996).

The large time behaviour of solutions to the following convection-diffusion problem, \[ u_t-\Delta u+a\nabla(|u|^{q-1}u)=0\quad{in }\mathbb{R}^n\times\mathbb{R}^+,\;n\geq 1,\;u(z,0)=u_0(z)\text{ in }\mathbb{R}^n, \] is considered. The case of nonnegative integrable \(u_0\) was considered in previous publications. In the present paper no sign restrictions to the initial value are imposed.

Reviewer: P.Y.Yalamov (Russe)

MSC:

35K55	Nonlinear parabolic equations
35K15	Initial value problems for second-order parabolic equations

Keywords:

no sign restrictions to the initial value

References:

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