Cauchy Problems for Semilinear Parabolic Equations in Grand Herz Spaces

Suixin He () and Ronghui Liu
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Suixin He: School of Mathematics and Statistics, Yili Normal University, Yining 835000, China
Ronghui Liu: Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China

Mathematics, 2025, vol. 13, issue 22, 1-12

Abstract: In this paper, we study Cauchy problems for the semilinear parabolic equations ∂ t u − ▵ u = G ( u ) with initial data in grand Herz spaces. We extend previous results established for classical Herz spaces to the broader framework of grand Herz spaces. The existence, uniqueness and stablity of solutions, as well as for their behaviour at small time are obtained by empolying heat kernel estimates, fixed-point theorems and some functional space theory.

Keywords: Cauchy problem; semilinear parabolic equation; grand Herz space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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