Deterministic particle approximation of aggregation-diffusion equations on unbounded domains

We consider a one-dimensional aggregation-diffusion equation, which is the gradient flow in Wasserstein space of functional with competing attractive-repulsive interactions. prove that fully deterministic particle approximations piecewise constant densities introduced [25] starting from general bounded initial converge strongly L 1 to unique weak solution PDE. In particular, result achieved unbounded domains and for arbitrary nonnegative densities, thus extending results [30] , [34] [35] (in no-vacuum condition required) giving an alternative approach [10] case, including also subquadratic superquadratic diffusions. provide numerical simulations approximation scheme.