A semilinear heat equation with a localized nonlinear source and non‐continuous initial data |
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| Authors: | Lucas C. F. Ferreira Elder J. Villamizar‐Roa |
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| Affiliation: | 1. Departamento de Matemática, Universidade Estadual de Campinas, , CEP, 13083‐859 Campinas‐SP, BrazilL.C.F. Ferreira was supported by CNPq and Fapesp‐SP, Brazil;2. Escuela de Matemáticas, Universidad Industrial de Santander, , A.A. 678 Bucaramanga, Colombia |
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| Abstract: | This paper is devoted to the study of the Cauchy problem for a semilinear heat equation with nonlinear term presenting a nonlinear source centered in a closed region of the spatial domain Ω. We assume that  is either a smooth bounded domain or the whole space  ,  The initial data  is assumed to belong to the Lebesgue space  . Copyright © 2011 John Wiley & Sons, Ltd. |
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| Keywords: | Nonlinear heat equations concentrated nonlinear source Lebesgue spaces |
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