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 \[ \rho (x,t)\partial u/\partial t=div(\lambda (x,t)\text{grad} u)+q(\tau)\psi (u,\tau),\quad \partial \tau /\partial t=\psi (u(x,t),\tau (x,t)). \]
Reviewer: T.A.Dzhangveladze


35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35K20 Initial-boundary value problems for second-order parabolic equations
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