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arXiv 1406.7307math.AP
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动力学湮没模型自相似轮廓的唯一性

Uniqueness of the self-similar profile for a kinetic annihilation model

Véronique Bagland, Bertrand Lods

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摘要：

我们证明了一个自相似解的存在性我们证明了一个修正的Boltzmann方程描述概率弹道湮灭的自相似轮廓解的唯一性。这样一个模型描述了一个硬球系统，当两个粒子相遇时，它们要么以$α\in (0,1)$的概率湮灭，要么以$1-α$的概率发生弹性碰撞。在我们先前的贡献（J.微分方程，254，3023- 3080，2013）中已经获得了小于显式门限值$\underlineα_1$的$α$的自相似轮廓的存在。.我们在这里补充了对此类模型的分析，表明对于某些$α^{\sharp} $显式，自相似轮廓对于$α\in (0,α^{\sharp})$是独特的。

英文摘要：

We show the existence of a self-similar solution for a We prove the uniqueness of the self-similar profile solution for a modified Boltzmann equation describing probabilistic ballistic annihilation. Such a model describes a system of hard spheres such that, whenever two particles meet, they either annihilate with probability $α\in (0,1)$ or they undergo an elastic collision with probability $1-α$. The existence of a self-similar profile for $α$ smaller than an explicit threshold value $\underlineα_1$ has been obtained in our previous contribution (J. Differential Equations, 254, 3023--3080, 2013). . We complement here our analysis of such a model by showing that, for some $α^{\sharp} $ explicit, the self-similar profile is unique for $α\in (0,α^{\sharp})$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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