This paper studies the locally bounded property of a generalized infinite particle system with zero range interactions and the dissipation of the resolvent operator of the system generator.

This paper consider a doubly nonlinear parabolic equations systems in diagonal form, under rather general structural conditions, proved that its generalized solution is bounded locally and globally.

By using the semigroup of bounded linear operator, a new locally convex vector topological is introduced, and some propositions of it are given.