Ornamental Grasses Dying

Could anyone tell me if I should dig these grasses out or will they recover like the lawn? Think it was due to the heat! Thanks

 

I have what appears to be the same sort of grass that's been living in a huge pot with an olive tree on my patio for well over 20 years.
I often forget to water the pot and my 2 look just like yours, but I know from previous years they do recover when I eventually remember to water. It does take several months, but they've always recovered in the past, so hoping they will this time too.
But no guarantees..

 

This is the same grass only much healthier not sure exactly what it is

 

They both looked worse a few weeks ago, the one on the left has started to recover.
But looks like I forgot to water again looking at the compost.
I don't know what the variety is.

 

@bluegeranium, it looks like an Carex Ice Dance (a type of sedge grass). Very drought tolerant, especially if in shade. If you take out any dead brown strands, that will let new growth come through. It is pretty indestructible, in my experience.

 

My grasses are the same I'd thought about trimming it to around 4 inch,sure I've seen them in garden centers like this throu out autumn /winter

 

Although Carexes can manage drier conditions once well established, they actually do best with wet conditions - ie soil that doesn't readily dry out.