Mathematics – Analysis of PDEs
Scientific paper
2010-11-21
J. Math. Anal. Appl. 379 (2011) 748-763
Mathematics
Analysis of PDEs
21 pages; published version with typos corrected
Scientific paper
A symmetry group method is used to obtain exact solutions for a semilinear radial heat equation in $n>1$ dimensions with a general power nonlinearity. The method involves an ansatz technique to solve an equivalent first-order PDE system of similarity variables given by group foliations of this heat equation, using its admitted group of scaling symmetries. This technique yields explicit similarity solutions as well as other explicit solutions of a more general (non-similarity) form having interesting analytical behavior connected with blow up and dispersion. In contrast, standard similarity reduction of this heat equation gives a semilinear ODE that cannot be explicitly solved by familiar integration techniques such as point symmetry reduction or integrating factors.
Ali Saqib
Anco Stephen C.
Wolf Thomas
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