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.
引用
收藏
页码：112 / 123
页数：12
相关论文
共 50 条
  • [1] SOME EXACT SOLUTIONS OF HEAT EQUATION
    MCDONALD, KL
    [J]. BULLETIN OF THE AMERICAN PHYSICAL SOCIETY, 1975, 20 (06): : 813 - 813
  • [2] Construction and Study of Exact Solutions to A Nonlinear Heat Equation
    Kazakov, A. L.
    Orlov, Sv. S.
    Orlov, S. S.
    [J]. SIBERIAN MATHEMATICAL JOURNAL, 2018, 59 (03) : 427 - 441
  • [3] Construction and Study of Exact Solutions to A Nonlinear Heat Equation
    A. L. Kazakov
    Sv. S. Orlov
    S. S. Orlov
    [J]. Siberian Mathematical Journal, 2018, 59 : 427 - 441
  • [4] Exact Solutions with Generalized Separation of Variables in the Nonlinear Heat Equation
    A. F. Barannyk
    T. A. Barannyk
    I. I. Yuryk
    [J]. Ukrainian Mathematical Journal, 2022, 74 : 330 - 349
  • [5] EXACT SOLUTIONS WITH GENERALIZED SEPARATION OF VARIABLES IN THE NONLINEAR HEAT EQUATION
    Barannyk, A. F.
    Barannyk, T. A.
    Yuryk, I. I.
    [J]. UKRAINIAN MATHEMATICAL JOURNAL, 2022, 74 (03) : 330 - 349
  • [6] Exact Solutions of the Nonlinear Equation
    Barannyk, A. F.
    Barannyk, T. A.
    Yuryk, I. I.
    [J]. UKRAINIAN MATHEMATICAL JOURNAL, 2018, 69 (09) : 1370 - 1378
  • [7] Exact Solutions with Generalized Separation of Variables of the Nonlinear Heat Equation with a Source
    Barannyk, Anatolii
    Barannyk, Tetyana
    Yuryk, Ivan
    [J]. UKRAINIAN MATHEMATICAL JOURNAL, 2024, 76 (02) : 192 - 213
  • [8] Reduction Method and New Exact Solutions of the Multidimensional Nonlinear Heat Equation
    A. A. Kosov
    E. I. Semenov
    [J]. Differential Equations, 2022, 58 : 187 - 194
  • [9] Reduction Method and New Exact Solutions of the Multidimensional Nonlinear Heat Equation
    Kosov, A. A.
    Semenov, E., I
    [J]. DIFFERENTIAL EQUATIONS, 2022, 58 (02) : 187 - 194
  • [10] New exact solutions for some power law nonlinear diffusion equation
    Layeni O.P.
    [J]. Journal of Applied Mathematics and Computing, 2011, 35 (1-2) : 93 - 102
12345