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differential equations - Piecewise causes ndnum warning in NDSolve


Bug introduced in 8.0.4 or earlier.




I try to solve the heat transfer equation with boundary condition that depends on time:


r0 = 0.75 10^-3;(*Beam spot size, m*)
ω = π ν;
ν = 1; (*pulse repetition rate, Hz*)

c = 1710;(*Heat capacity, W/(m·K)*)
ρ = 879; (*Density, kg/m^3*)
λ = 0.111;(*Heat conductivity, W/(m·K)*)
T0 = 300;(*initial temperature,K*)

T1 = 1000 - T0; (*Hot state temperature, K*)
Rm = 3 10^-3;(*Sample Radius, m*)
zm = 2 10^-3 ;(*Sample thickness, m*)   

 eq = D[T[R, z, t], t] == λ/(
    c ρ) (1/(R + 10^-20) D[R D[T[R, z, t], R], R] + 
      D[T[R, z, t], {z, 2}]);

init1 = T[R, z, 0] == T0;
bc1 = D[T[R, z, t], {R, 1}] == 0 /. R -> 0;

bc2 = D[T[R, z, t], {R, 1}] == 0 /. R -> Rm;
bc3 = T[R, z, t] == 
    Piecewise[{{T0 + T1 (1 - Abs@Sin[ω t])^500, 
       0 <= R <= r0}, {T0, True}}] /. z -> 0;
bc4 = T[R, z, t] == T0 /. z -> zm;

sol = NDSolveValue[{eq, init1, bc1, bc2, bc3, bc4}, 
  T[R, z, t], {R, 0, Rm}, {z, 0, zm}, {t, 0, 10},
  AccuracyGoal -> 30, MaxStepFraction -> 0.05]


The piecewise function defines the temperature at the left side of the z-interval as a short square pulses coming with frequency ω to central part of the disk.


However, solver returns the error-messages:



NDSolveValue::ibcinc: Warning: boundary and initial conditions are inconsistent. NDSolveValue::ndnum: Encountered non-numerical value for a derivative at t == 0.



What's wrong? I've tried with FEM package but it produce even more error-messages :)




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