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**Degenerate operators**## The Kate Edger Department of Mathematics

# Degenerate operators

The aim of this project is to understand the mathematical concepts behind the evolution of heat in materials when the heat conductivity is not uniform over the material.

When the conductivity is positive, but not necessarily smooth, the heat flow is well understood.

Similarly, if the conductivity is smooth, but vanishes at some parts of the material, then the heat evolution is fairly well understood.

The novelty of this project is to understand the global behaviour of heat flow if the conductivity is both non-smooth and may vanish on some parts. Then insulation may occur.

Research is supported by the New Zealand Marsden Fund.

### Researchers at The University of Auckland

- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
- New Zealand Journal of Mathematics

**Programmes, Centres and Partners**

- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
- New Zealand Journal of Mathematics

**Programmes, Centres and Partners**