Global solutions of semilinear heat equations in Hilbert spaces

Abstract

The existence, uniqueness, regularity and asymptotic behavior of global solutions of semilinear heat equations in Hilbert spaces are studied by developing new results in the theory of one-parameter strongly continuous semigroups of bounded linear operators. Applications to special semilinear heat equations in $L^2\left({ℝ}^n\right)$ governed by pseudo-differential operators are given.