ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35 Nanbu, Tokumori, Toyama Medical and Pharmaceutical University, Japan On solutions of some nonlinear degenerate parabolic equations We consider the large time behaviour of solutions of the initial-boundary value problem for some nonlinear degenearte parabolic equations @u_{t} = Δ_{x}(A(u)) + b · ∇(B(u)) − q(x, t)C(u) where u = u(x, t) is a scalar function of the spatial variable x ∈ Ω and time t > 0, b ∈ R^{N}(b ≠ O) and Ω is an open regular domain in R^{N}. Here the functions A(u), B(u), C(u) satisfy A(0) = A′(0) = 0, A′(u) > 0 (u ≠ 0), B(0) = B′(0) = 0 , C(0) = C′(0) = 0 and some suitable conditions.