On some exact solutions of the nonlinear heat equation

被引：0
|
作者：
Kazakov, A. L. [1 ,2 ,3 ]
Orlov, S. S. [1 ,2 ,3 ]
机构：
[1] Russian Acad Sci, Siberian Branch, Matrosov Inst Syst Dynam & Control Theory, Phys Mat Sci, Irkutsk, Russia
[2] Russian Acad Sci, Siberian Branch, Matrosov Inst Syst Dynam & Control Theory, Irkutsk, Russia
[3] Russian Acad Sci, Siberian Branch, Matrosov Inst Syst Dynam & Control Theory, Lab, Irkutsk, Russia
来源：
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN | 2016年 / 22卷 / 01期
关键词：
partial differential equations; nonlinear heat (filter) equation; invariant solution; Cauchy problem;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The paper is devoted to finding invariant solutions of the nonlinear heat (filter) equation without sources or sinks in the case of one spatial variable and a power dependence of the thermal conduction coefficient on the temperature. The construction procedure is reduced to Cauchy problems for ordinary differential equations with a singularity at the highest derivative. An existence and uniqueness theorem is proved for solutions of such problems in the class of analytic functions (in the form of a converging series). An estimate is obtained for the convergence domain of this series in one particular case.
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页码：112 / 123
页数：12
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