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
  • [31] Exact solutions of a nonpolynomially nonlinear Schrodinger equation
    Parwani, R.
    Tan, H. S.
    [J]. PHYSICS LETTERS A, 2007, 363 (03) : 197 - 201
  • [32] Exact solutions to the nonlinear equation in traffic congestion
    Cheng Li
    Damin Cao
    Qing Du
    [J]. Advances in Difference Equations, 2020
  • [33] Exact solutions for nonlinear foam drainage equation
    E. M. E. Zayed
    Abdul-Ghani Al-Nowehy
    [J]. Indian Journal of Physics, 2017, 91 : 209 - 218
  • [34] The exact solutions for a nonisospectral nonlinear Schrodinger equation
    Ning, Tong-ke
    Zhang, Weiguo
    Jia, Gao
    [J]. CHAOS SOLITONS & FRACTALS, 2009, 42 (02) : 1100 - 1105
  • [35] New Exact Solutions for a Nonlinear Lattice Equation
    Wu, Chufen
    Weng, Peixuan
    [J]. SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2009, 33 (03) : 587 - 596
  • [36] New exact solutions of a nonlinear integrable equation
    Yildiz, Guldem
    Daghan, Durmus
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (11) : 6761 - 6770
  • [37] Exact solutions to the nonlinear equation in traffic congestion
    Li, Cheng
    Cao, Damin
    Du, Qing
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
  • [38] Exact solutions of a nonlocal nonlinear Schrodinger equation
    Gao, Hui
    Xu, Tianzhou
    Yang, Shaojie
    Wang, Gangwei
    [J]. OPTOELECTRONICS AND ADVANCED MATERIALS-RAPID COMMUNICATIONS, 2016, 10 (9-10): : 651 - 657
  • [39] EXACT-SOLUTIONS TO A COUPLED NONLINEAR EQUATION
    GUHAROY, C
    [J]. INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 1988, 27 (04) : 447 - 450
  • [40] Exact Solutions of the Equation of a Nonlinear Conductor Model
    Aristov, A. I.
    [J]. DIFFERENTIAL EQUATIONS, 2020, 56 (09) : 1113 - 1118
12345