On properties of the asymptotic expansion of the heat trace for the N/D   problem
  The spectral problem where the field satisfies Dirichlet conditions on one part of the boundary of the relevant domain and Neumann on the remainder is discussed. It is shown that there does not exist a classical asymptotic expansion for short time in terms of fractional powers of $t$ with locally computable coefficients. 
Stuart Dowker, Peter Gilkey and Klaus Kirsten