The heat equation with singular nonlinearity and singular initial data |
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Authors: | M. Loayza |
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Affiliation: | Departamento de Matemática, Universidade Federal de Pernambuco, 50740-540 Recife, PE, Brazil |
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Abstract: | We study the existence, uniqueness and regularity of positive solutions of the parabolic equation ut−Δu=a(x)uq+b(x)up in a bounded domain and with Dirichlet's condition on the boundary. We consider here a∈Lα(Ω), b∈Lβ(Ω) and 0<q?1<p. The initial data u(0)=u0 is considered in the space Lr(Ω), r?1. In the main result (0<q<1), we assume a,b?0 a.e. in Ω and we assume that u0?γdΩ for some γ>0. We find a unique solution in the space . |
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Keywords: | Heat equation Existence Uniqueness Concave-convex nonlinearity Singular initial data |
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