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
  • [41] Exact solutions for nonlinear foam drainage equation
    Zayed, E. M. E.
    Al-Nowehy, A-G
    [J]. INDIAN JOURNAL OF PHYSICS, 2017, 91 (02) : 209 - 218
  • [42] Symmetries for exact solutions to the nonlinear Schrodinger equation
    Aktosun, Tuncay
    Busse, Theresa
    Demontis, Francesco
    van der Mee, Cornelis
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (02)
  • [43] Exact Solutions of the Equation of a Nonlinear Conductor Model
    A. I. Aristov
    [J]. Differential Equations, 2020, 56 : 1113 - 1118
  • [44] EXACT-SOLUTIONS TO A NONLINEAR DIFFUSION EQUATION
    KING, JR
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1991, 24 (14): : 3213 - 3216
  • [45] Exact solutions to the focusing nonlinear Schrodinger equation
    Aktosun, Tuncay
    Demontis, Francesco
    van der Mee, Cornelis
    [J]. INVERSE PROBLEMS, 2007, 23 (05) : 2171 - 2195
  • [46] Bifurcations and Exact Solutions in a Nonlinear Wave Equation
    Li, Zongguang
    Liu, Rui
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2019, 29 (07):
  • [47] Exact Solutions to One Nonlinear Sobolev Equation
    A. I. Aristov
    [J]. Moscow University Computational Mathematics and Cybernetics, 2019, 43 (4) : 156 - 165
  • [48] On the exact controllability of a nonlinear stochastic heat equation
    Ton, Bui An
    [J]. ABSTRACT AND APPLIED ANALYSIS, 2006,
  • [49] Bifurcations and Exact Solutions of the Nonlinear Schrodinger Equation with Nonlinear Dispersion
    Zhang, Qiuyan
    Zhou, Yuqian
    Li, Jibin
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2022, 32 (03):
  • [50] On the integrability and exact solutions of the nonlinear diffusion equation with a nonlinear source
    Vijayakumar, K
    [J]. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES B-APPLIED MATHEMATICS, 1998, 39 : 513 - 527
12345