Back to the Keller-Osserman Condition for Boundary Blow-up Solutions
Back to the Keller-Osserman Condition for Boundary Blow-up Solutions
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DOI：
10.1515/ans-2007-0205
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发表时间：
2007-05
影响因子：
1.8
通讯作者：
S. Dumont;L. Dupaigne;O. Goubet;Vicentiu D. Rădulescu
中科院分区：
文献类型：
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作者：
S. Dumont;L. Dupaigne;O. Goubet;Vicentiu D. Rădulescu
本文讨论椭圆型偏微分方程解Δu=f(U)的边界爆破解的存在唯一性和数值逼近，其中f满足所谓的Keller-Osserman条件。作为例子，我们构造了球上方程Δu=U2(1+cos u)的边界爆破解的无穷族。我们证明了当f在无穷大邻域内递增和凸时(在球上)的唯一性，并讨论并执行了一些数值计算来逼近这样的边界爆破解。
Abstract This article is concerned with the existence, uniqueness and numerical approximation of boundary blow up solutions for elliptic PDE’s Δu = f(u), where f satisfies the so-called Keller-Osserman condition. We characterize existence of such solutions for non-monotone f. As an example, we construct an infinite family of boundary blow up solutions for the equation Δu = u2(1 + cos u) on a ball. We prove uniqueness (on balls) when f is increasing and convex in a neighborhood of infinity and we discuss and perform some numerical computations to approximate such boundary blow-up solutions.