Material under sinks - what to replace with?

[darael]

There is what I can best describe as a self adhesive rubber mat under my kitchen sink that is peeling away. what is this called and can it be preferably replaced, if not repaired?

 

[darael]

I am talking about the black material underneath the sink when you look in the cupboard, not at the bottom of the usable sink.

The sink was put in not too long ago, so asbestos shouldn't be a concern.

I don't know why the material is already coming away. If I were to glue back what is there, what glue would I use or doesn't it matter too much?

 

[darael]

Can't see that sticking it back down very well!

To be honest, all you would see in a photo taken from the kitchen cupboard, is the underneath of a sink with something black and what should be flat hanging down.