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On the solution of the heat equation with nonlinear unbounded memory. (English) Zbl 0602.35056
The author studies the uniqueness and existence of the solution of the boundary value problem for the following system of nonlinear partial differential equations $\rho (x,t)\partial u/\partial t=div(\lambda (x,t)\text{grad} u)+q(\tau)\psi (u,\tau),\quad \partial \tau /\partial t=\psi (u(x,t),\tau (x,t)).$