Bachelor project presentation: Vlad Malai

Speaker:
Vlad Malai

Title:
Local and Global Symmetries of PDE's

Abstract:
We look into the theoretical framework developed by Sophus Lie in his study of differential equations, and determine correspondingly, using the developed techniques, the known Lie point symmetries of several PDEs: logistic equation, Schrödinger equation, Burgers' equation. Subsequently we look whether the local symmetry group can be extended to a global one. The analysis of the Schrödinger equation shows that its symmetries form a global group under Craddock's theorem and in the case of Burgers' equation one can use a 1-1 mapping to the solutions of the heat equation to establish a globalization theorem. We end by mentioning an example from the literature, a specific filtration equation, for which non- globalizable symmetries have been found.

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