Semilinear parabolic equations in Herz spaces

Abstract

In this paper, we will study local and global Cauchy problems for the semilinear parabolic equations with initial data in Herz spaces. These spaces unify and generalize many classical function spaces such as Lebesgue spaces of power weights. Our results cover the results obtained with initial data in Lebesgue spaces. Moreover, the results in Herz spaces are a little different from the results in Lebesgue spaces.