ON ASYMPTOTIC “EIGENFUNCTIONS” OF THE CAUCHY PROBLEM FOR A NONLINEAR PARABOLIC EQUATION
ON ASYMPTOTIC “EIGENFUNCTIONS” OF THE CAUCHY PROBLEM FOR A NONLINEAR PARABOLIC EQUATION
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DOI：
10.1070/sm1986v054n02abeh002979
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发表时间：
1986-02
期刊：
影响因子：
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通讯作者：
V. Galaktionov;S. Kurdyumov;A. Samarskii
中科院分区：
文献类型：
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作者：
V. Galaktionov;S. Kurdyumov;A. Samarskii
研究了一类半线性抛物型方程Cauchy问题解的渐近性。建立了具有不同自相似解的无穷集合（连续统）的存在性，其形式为，，其中函数满足一个常微分方程。建立了这些解的渐近稳定的条件。结果表明，对于近似自相似解（ap.s -s.s）所描述的问题，存在与热方程的一类自相似解重合的解，而对于和ap.s -s.s。有where的形式。人物:2。参考书目：78种。
The asymptotic () behavior of solutions of the Cauchy problem is studied for the semilinear parabolic equation where and as . The existence is established of an infinite collection (a continuum) of distinct self-similar solutions of the form , , where the function satisfies an ordinary differential equation. Conditions for the asymptotic stability of these solutions are established. It is shown that for there exist solutions of the problem whose behavior as is described by approximate self-similar solutions (ap.s.-s.s.'s) which in the case coincide with a family of self-similar solutions of the heat equation , while for and the ap.s.-s.s. has the form where .Figures: 2. Bibliography: 78 titles.