For theta >= 1, the empirical density of the symmetric zero-range process with slow boundary reservoirs converges in probability to the unique weak solution of the nonlinear heat equation with Robin (theta = 1) or Neumann (theta > 1) boundary conditions.
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Hydrodynamic Limit of the Symmetric Zero-Range Process with Slow Boundary
For theta >= 1, the empirical density of the symmetric zero-range process with slow boundary reservoirs converges in probability to the unique weak solution of the nonlinear heat equation with Robin (theta = 1) or Neumann (theta > 1) boundary conditions.