Multidimensional exact solutions to a quasilinear parabolic equation with anisotropic heat conductivity

被引：1

作者：

Semenov, EI ^{[1
]}

机构：

[1] Inst Syst Dynam & Control Theory, Irkutsk, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2006年 / 47卷 / 02期

关键词：

quasilinear parabolic heat equation; Liouville equation; multidimensional exact solution; equivalence transformation; anisotropy; conjugate harmonic function;

D O I：

10.1007/s11202-006-0049-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove invariance of a quasilinear parabolic equation with anisotropic heat conductivity in the three-dimensional coordinate space under some equivalence transformations and present some explicit formulas for these transformations. We consider nontrivial reductions of the equation to similar equations of less spatial dimension. Using these results, we construct new exact multidimensional solutions to the equation which depend on arbitrary harmonic functions.

引用

页码：376 / 382

页数：7

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