### Solutions in Morrey spaces of some semilinear heat equations with time-dependent external forces

Xiaofang Zhou
Source: Nagoya Math. J. Volume 174 (2004), 127-163.

#### Abstract

In this paper, we consider the Cauchy problem for some semilinear heat equations with time-dependent external forces. Both the external force and the initial data are assumed to be small in some Morrey spaces. We first prove the unique existence of a small time-global solution. We next show the stability of that solution by proving the time-global sovability of perturbation problems.

First Page:
Primary Subjects: 35K55
Secondary Subjects: 35B35, 35K15
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.nmj/1114632069
Mathematical Reviews number (MathSciNet): MR2066106
Zentralblatt MATH identifier: 1053.35062

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