We consider the following nonlinearly perturbed version of the elliptic-parabolic system of Keller-Segel type: ∂tu - Δu + ∇ = (u∇v) = 0, t > 0, x ∈ ℝ2, -Δv +v -vp = u, t > 0, x ∈ ℝ2, u(0, x) = u 0(x:) ≥ 0, x ∈ ℝ2, where 1 < p < ∞. It has already been shown that the system admits a positive solution for a small nonnegative initial data in L1(ℝ2) ∩ L2(ℝ2) which corresponds to the local minimum of the associated energy functional to the elliptic part of the system. In this paper, we show that for a radially symmetric nonnegative initial data, there exists another positive solution which corresponds to the critical point of mountain-pass type. The υ-component of the solution bifurcates from the unique positive radially symmetric solution of -Δw + w = wp in ℝ2.
|ジャーナル||Electronic Journal of Differential Equations|
|出版ステータス||Published - 2009 1月 2|
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