Zhou, Xiaofang Solutions in Morrey spaces of some semilinear heat equations with time-dependent external forces. (English) Zbl 1053.35062 Nagoya Math. J. 174, 127-163 (2004). It is considered the Cauchy problem for a semilinear heat equation with time-dependent external forces \[ {\partial v\over \partial t}(t,x)=\Delta v(t,x)+v(t,x)^\nu+f(t,x)\quad\text{in}\quad (0,\infty)\times {\mathbb R}^n, \]\[ v(0,x)=a(x)\quad\text{on}\quad {\mathbb R}^n \] with \(\nu\geq 3,\) \(\nu\in {\mathbb Z}.\) Both the external force and the initial data are assumed to be small in some Morrey spaces. It is proved unique existence of a small time-global solution. The stability of that solution follows by the time-global solvability of perturbation problems. Reviewer: Lubomira Softova (Bari) MSC: 35K55 Nonlinear parabolic equations 35B35 Stability in context of PDEs 35K15 Initial value problems for second-order parabolic equations Keywords:small time-global solution; Cauchy problem PDFBibTeX XMLCite \textit{X. Zhou}, Nagoya Math. J. 174, 127--163 (2004; Zbl 1053.35062) Full Text: DOI References: [1] J. Math. Sci. Univ. Tokyo 6 pp 793– (1999) [2] DOI: 10.1080/00036818408839514 · Zbl 0582.35060 · doi:10.1080/00036818408839514 [3] DOI: 10.1007/BF02498228 · Zbl 0919.35054 · doi:10.1007/BF02498228 [4] DOI: 10.1007/BF02761845 · Zbl 0476.35043 · doi:10.1007/BF02761845 [5] DOI: 10.1080/03605309208820892 · Zbl 0771.35047 · doi:10.1080/03605309208820892 [6] Indiana Univ. Math. J. 44 pp 1307– (1995) [7] DOI: 10.1007/BF02414340 · Zbl 0149.09102 · doi:10.1007/BF02414340 [8] DOI: 10.1080/03605309408821042 · Zbl 0803.35068 · doi:10.1080/03605309408821042 [9] DOI: 10.1016/S0362-546X(00)85031-2 · Zbl 0953.35013 · doi:10.1016/S0362-546X(00)85031-2 [10] Acad. Sci. Paris, Sér. I 317 pp 1127– (1993) [11] Semilinear heat equations with measures as initial data (1986) [12] DOI: 10.2969/jmsj/02930407 · Zbl 0353.35057 · doi:10.2969/jmsj/02930407 [13] DOI: 10.1214/aop/1176989278 · Zbl 0776.60038 · doi:10.1214/aop/1176989278 [14] DOI: 10.3792/pja/1195519254 · Zbl 0281.35039 · doi:10.3792/pja/1195519254 [15] DOI: 10.3792/pjaa.71.199 · Zbl 0853.35088 · doi:10.3792/pjaa.71.199 [16] DOI: 10.1512/iumj.1982.31.31016 · Zbl 0465.35049 · doi:10.1512/iumj.1982.31.31016 [17] J. Fac. Sci. Univ. Tokyo, I 13 pp 109– (1966) [18] J. Math. Pure. Appl. (9) 62 pp 73– (1983) [19] Funkcial. Ekvac 43 pp 419– (2000) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.