Group analysis of \((2+1)\)- and \((3+1)\)-dimensional diffusion-convection equations (Q947541)
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scientific article; zbMATH DE number 5349069
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Group analysis of \((2+1)\)- and \((3+1)\)-dimensional diffusion-convection equations |
scientific article; zbMATH DE number 5349069 |
Statements
Group analysis of \((2+1)\)- and \((3+1)\)-dimensional diffusion-convection equations (English)
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6 October 2008
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The aim of the article is to carry out the group classification of the \((2+1)\)-dimensional convection equation \(u_t=(D(u)u_x)_x+(F(u)u_y)_y+K(u)u_x\) and the \((3+1)\)-dimensional one \(u_t=(D(u)u_x)_x+(F(u)u_y)_y+(G(u)u_z)+K(u)u_x\) with arbitrary smooth functions \(F(u)\neq 0,G(u)\neq 0\) and \(D^2(u)+K^2(u)\neq 0\), completing the previously existing results. The obtained Lie symmetries are used for the construction of similarity reductions and obtaining exact solutions in partial cases of the equations considered.
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diffusion-convection equations
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equivalence transformations
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Lie symmetries
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similarity reductions
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