A retarded semilinear heat equation with polynomial-growth nonlinearities and a dissipative structure has unique global solutions, exponential decay, and H2 regularity for solution exponents above a computable threshold.
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Global Estimates and Regularity of Retarded Parabolic Equations with Fast-growing Nonlinearities
A retarded semilinear heat equation with polynomial-growth nonlinearities and a dissipative structure has unique global solutions, exponential decay, and H2 regularity for solution exponents above a computable threshold.