The Cauchy problem for heat equations with exponential nonlinearity

Abstract

The Cauchy problem for the semilinear heat equations is studied in the Orlicz space exp L 2 ( R n ) , where any power behavior of interaction works as a subcritical nonlinearity. We prove the existence of global solutions for the semilinear heat equations with the exponential nonlinearity under the smallness condition on the initial data in exp L 2 ( R n ) .