Symmetry analysis and exact solutions of semilinear heat flow in multi-dimensions

Please always quote using this URN: urn:nbn:de:0297-zib-13213
  • 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.

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Author:Stephen S. Anco, S. Ali, Thomas Wolf
Document Type:ZIB-Report
Tag:semilinear heat equation, similarity reduction, exact solutions, group foliation, symmetry
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS
35-XX PARTIAL DIFFERENTIAL EQUATIONS
58-XX GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](For geometric integration theory, see 49Q15)
Date of first Publication:2011/06/23
Series (Serial Number):ZIB-Report (11-26)
Published in:Appeared in: Journal of Mathematical Analysis and Applications, 379 (2011), 748-763.