In this work, we study the Prigozhin model for growing sandpile with mixed boundary conditions and an arbitrary time dependent angle of repose. On one part of the boundary the homogeneous Dirichlet boundary condition is provided, on the other one the Robin condition is used. Using the implicit Euler discretization in time, we prove the existence and uniqueness of variational solution of the model and for the numerical analysis we use a duality approach

growing sandpile; Fourier boundary condition; nonlinear semi-group; Dirichlet boundary condition; Euler discretization in time