Reduction operators of variable coefficient semilinear diffusion equations with an exponential source

O. O. Vaneeva; R. O. Popovych; C. Sophocleous

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arXiv · 1010.2046

Reduction operators of variable coefficient semilinear diffusion equations with an exponential source

O. O. Vaneeva·R. O. Popovych·C. Sophocleous

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Abstract

Reduction operators (called also nonclassical or $Q$-conditional symmetries) of variable coefficient semilinear reaction-diffusion equations with exponential source $f(x)u_t=(g(x)u_x)_x+h(x)e^{mu}$ are investigated using the algorithm involving a mapping between classes of differential equations, which is generated by a family of point transformations. A special attention is paid for checking whether reduction operators are inequivalent to Lie symmetry operators. The derived reduction operators are applied to construction of exact solutions.

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BibTeX RIS

O. O. Vaneeva, R. O. Popovych, C. Sophocleous. 2010-10-11. Reduction operators of variable coefficient semilinear diffusion equations with an exponential source. https://arxiv.org/abs/1010.2046

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