Nonstabilizing solutions and grow-up set for a supercritical semilinear diffusion equation
Nonstabilizing solutions and grow-up set for a supercritical semilinear diffusion equation
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DOI：
10.57262/die/1356060346
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发表时间：
2004-01
影响因子：
1.4
通讯作者：
P. Polácik;E. Yanagida
中科院分区：
文献类型：
--
作者：
P. Polácik;E. Yanagida
本文研究的是超临界半线性扩散方程。我们证明了存在一种解决方案，该解决方案经历了在任意规定的位置和高度出现的单峰的生灭过程。特别是，当时间接近无穷大时，解没有渐近径向对称中心。我们还构建了一个具有任意规定的成长集的解决方案。
This paper is concerned with a supercritical semilinear diffusion equation. We show the existence of a solution that undergoes a birth-and-death process of a single peak emerging at arbitrarily prescribed positions and heights. In particular the solution has no asymptotic center of radial symmetry as time approaches infinity. We also construct a solution with arbitrarily prescribed grow-up set.