Abstract
We investigate the conditional symmetry of a multidimensional nonlinear reaction–diffusion equation by its reduction to a radial equation. We construct exact solutions of this equation and infinite families of exact solutions for the corresponding one-dimensional diffusion equation.
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REFERENCES
L. V. Ovsyannikov, Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978).
V. I. Fushchich, I. M. Shtelen', and N. I. Serov, Symmetry Analysis and Exact Solutions of Nonlinear Equations of Mathematical Physics [in Russian], Naukova Dumka, Kiev (1989).
V. A. Dorodnitsyn, I. V. Knyazeva, and S. R. Svirshchevskii, “Group properties of a heat-conduction equation with source in two-and three-dimensional cases,” Differents. Uravn., 19, No. 7, 1215–1224 (1983).
V. I. Fushchich and N. I. Serov, “Conditional invariance and reduction of a nonlinear heat-conduction equation,” Dopov. Akad. Nauk Ukr. SSR, No. 7, 24–28 (1990).
P. Clarkson and E. Mansfield, “Symmetry reductions and exact solutions of a class of nonlinear heat equations,” Physica D, 70, 250–288 (1993).
A. G. Nikitin and R. J. Wiltshire, “Systems of reactionJędrysekdiffusion equations and their symmetry properties”, J. Math. Phys., 42, No. 4, 1667–1688 (2001).
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Barannyk, T.A. Conditional Symmetry and Exact Solutions of a Multidimensional Diffusion Equation. Ukrainian Mathematical Journal 54, 1715–1721 (2002). https://doi.org/10.1023/A:1023740505453
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DOI: https://doi.org/10.1023/A:1023740505453