  We analyze the dynamical chiral symmetry breaking in gauge theory with the
nonperturbative renormalization group equation (NPRGE), which is a first order
nonlinear partial differential equation (PDE). In case that the spontaneous
chiral symmetry breaking occurs, the NPRGE encounters some non-analytic
singularities at the finite critical scale even though the initial function is
continuous and smooth. Therefore there is no usual solution of the PDE beyond
the critical scale. In this paper, we newly introduce the notion of a weak
solution which is the global solution of the weak NPRGE. We show how to
evaluate the physical quantities with the weak solution.
