Abstract

This article discusses the existence of global and blow-up solutions for the semilinear heat equation with a variable exponent. The equation is given by (Formula presented.) in (Formula presented.) with zero Dirichlet boundary condition and initial data in (Formula presented.). Our analysis covers both bounded and unbounded domains, (Formula presented.) is a continuous function in ? with (Formula presented.), (Formula presented.) and (Formula presented.). Our findings have significant implications as they improve upon the blow-up result discovered by Castillo and Loayza in Comput. Math. App. 2017;74(3):351–359 when (Formula presented.). © 2025 Informa UK Limited, trading as Taylor & Francis Group.