Evolution PDE with elliptic dissipative terms: critical index for singular initial data, self-similar solutions and analytic regularity

Abstract

We investigate the influence of the elliptic dissipative terms of evolution equations in ℝ n and T n on the critical L p , 1 ≤ p ≤ ∞, index of the singularity of the initial data, the analytic regularity for positive time and the existence of self-similar solutions.