Self-similarity and uniqueness of solutions for semilinear reaction-diffusion systems
Self-similarity and uniqueness of solutions for semilinear reaction-diffusion systems
复制标题
半线性反应扩散系统解的自相似性和唯一性
DOI：
10.57262/ade/1355854764
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发表时间：
2010
影响因子：
1.4
通讯作者：
Éder Mateus
中科院分区：
文献类型：
--
作者：
L. Ferreira;Éder Mateus
研究了Marcinkiewicz空间L(p1,∞)（Ω）×L(p2,∞)（Ω）中耦合半线性反应扩散系统初值问题的适定性。选择初值空间的指数p1， p2，以允许存在自相似解（当Ω = Rn）。作为耦合项估计的一个非平凡结果，我们证明了尺度不变类C（[0,∞）解的唯一性；Lp1（Ω） × Lp2（Ω）)，不管它们的大小和符号。我们还分析了解的渐近稳定性，证明了每个自相似解存在一个吸引池，并且Lp1 ×Lp2中的解表现出简单的长时间行为。
We study the well-posedness of the initial value problem for a coupled semilinear reactiondiffusion system in Marcinkiewicz spaces L(p1,∞)(Ω)×L(p2,∞)(Ω). The exponents p1, p2 of the initial value space are chosen to allow the existence of self-similar solutions (when Ω = Rn). As a nontrivial consequence of our coupling-term estimates, we prove the uniqueness of solutions in the scaling invariant class C([0,∞);Lp1(Ω) × Lp2(Ω)) regardless of their size and sign. We also analyze the asymptotic stability of the solutions, show the existence of a basin of attraction for each self-similar solution and that solutions in Lp1 ×Lp2 present a simple long time behavior.