Stabilization of solutions of the diffusion equation with a non-lipschitz reaction term

Kousuke Kuto

研究成果: Conference article

抜粋

In this paper we are concerned with the reaction-diffusion equation ut = Δu + f(u) in a ball of RN with Dirichlet boundary condition. We assume that f satisfies the concave-convex condition. A typical example is f(u) = |u|q-1u + |u|p-1u (0 < q < 1 < p < (N+2)/(N-2)). First we obtain the complete structure of positive solutions to the stationary problem; Δφ + f(φ) = 0. Next we state the relations between this structure and time-depending behaviors of nonnegative solutions (global existence or blow up) to the non-stationary problem.

元の言語English
ページ(範囲)789-800
ページ数12
ジャーナルNonlinear Analysis, Theory, Methods and Applications
47
発行部数2
DOI
出版物ステータスPublished - 2001 8 1
イベント3rd World Congres of Nonlinear Analysts - Catania, Sicily, Italy
継続期間: 2000 7 192000 7 26

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ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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