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• W2066798001 abstract "In this paper we investigate an abstract inverse problem that can be applied to the evolution equation ut(t,x)=Δu(t,x)+∫0tk(t−s)Δu(s,x)ds+∫Ωut(t,x)dx+F(u(t,x),∇u(t,x)) given suitable initial-boundary conditions. Here F is a given function and in the case F(u(t,x),∇u(t,x))=eu(t,x) the evolution equation has applications in the theory of combustion. Since we identify the convolution memory kernel k and the temperature u we associate an additional measurement on the temperature of type ∫Ωφ(x)u(t,x)dx=g(t), where φ and g are given functions. The novelty with respect to the existing literature is the presence of the term ∫Ωut(t,x)dx in the evolution equation that is motivated by a model in the theory of combustion. We prove a local in time existence theorem and a global in time uniqueness result." @default.
• W2066798001 created "2016-06-24" @default.
• W2066798001 creator A5013902247 @default.
• W2066798001 date "2007-12-01" @default.
• W2066798001 modified "2023-09-25" @default.
• W2066798001 title "An inverse problem for a parabolic integrodifferential model in the theory of combustion" @default.
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• W2066798001 doi "https://doi.org/10.1016/j.physd.2007.07.012" @default.
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