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Tarzia, Mahdi Boukrouche","submitted_at":"2016-10-05T23:05:35Z","abstract_excerpt":"We consider the non-classical heat conduction equation, in the domain $D=\\br^{n-1}\\times\\br^{+}$, for which the internal energy supply depends on an integral function in the time variable of % $(y , t)\\mapsto \\int_{0}^{t} u_{x}(0 , y , s) ds$, %where $u_{x}(0 , y , s)$ is the heat flux on the boundary $S=\\partial D$, with homogeneous Dirichlet boundary condition and an initial condition. The problem is motivated by the modeling of temperature regulation in the medium. 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