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This paper is concerned with global estimates and regularity of solutions forthe initial value problem of the retarded parabolic equation $$\frac{\patialu}{\patial t}-\Delta u=f(x,u)+g(u(x,t-r_1(t)),\cdots,u(x,t-r_m(t)))+h(x,t)$$ ina bounded domain $\Omega\subset R^n$ with fast-growing nonlinearities and adissipative structure, which is associated with the homogeneous Dirichletboundary condition. Our results reveal some deeper inherent connections betweendissipative structures and the regularity of solutions for such problems.

Global Estimates and Regularity of Retarded Parabolic Equations with Fast-growing Nonlinearities