In this paper, we investigate the stability of a degenerate heat equation ut(x,t)=(xαux(x,t))x,x∈(0,1),t>0in a non-cylindrical/cylindrical domain. It is well known that the heat equation without degeneracy is exponentially stable in cylindrical domain. In the case of degeneracy, we first extend the existing result  on uniform exponential stability in cylindrical domain from α∈ (0 , 1) to α∈ (0 , 2 ]. For a class of non-cylindrical domain (linear moving boundary), we show that the stability depends on the degeneration index α. More precisely, it is not exponentially stable for α= 0 , 1 but polynomially stable for α= 1 , is analogously exponentially stable for 1 < α< 2 , and is exponentially stable for α= 2. It is interesting to see that there is a positive impact of the degeneracy on stability of the system in non-cylindrical domain.
- Degenerate heat equation
- Non-cylindrical domain