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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:379

Article

Anco, Stephen C.¹  Ali, S.²  Wolf, Thomas¹ 

[1] Brock Univ, Dept Math, St Catharines, ON L2S 3A1, Canada

[2] Natl Univ Sci & Technol, Sch Elect Engn & Comp Sci, Islamabad 44000, Pakistan

关键词: Semilinear heat equation;    Similarity reduction;    Exact solutions;    Group foliation;    Symmetry;   

DOI  :  10.1016/j.jmaa.2011.01.073

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free