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heat equation; nonlinear unbounded memory; uniqueness; existence; boundary value problem

References:

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[2] E. Rastrup: **Heat of hydration of conrete**. Magazine of Concrete Research, v. 6, no 17, 1954.

[3] K. Rektorys : **Nonlinear problem of heat conduction in concrete massives**. (In Czech), Thesis MÚ ČSAV, Praha 1961.

[4] K. Rektorys: **The method of discretization in time and partial differential equations**. Reidel Co, Dodrecht, Holland 1982. MR 0689712 | Zbl 0522.65059

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[9] A. Doktor: **Mixed problem for semilinear hyperbolic equation of second order with Dirichlet boundary condition**. Czech. Math. J., 23 (98), 1973, 95-122. MR 0348276 | Zbl 0255.35061