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Parabolic partial differential equations with memory. (English) Zbl 0615.35045
The paper deals with the system of parabolic equations \[ \partial u^{(r)}/\partial t+A_ r u^{(r)}=f^{(r)}(t,x,Du,\int^{t}_{0}K_ a(t,\tau)Du(\tau)d\tau) \] for \(r=1,2,...,N\) in domain \(\Omega\times (0,T)\), where \(A_ r\) denotes an elliptic operator. The existence, uniqueness and some properties of the solution are proved. An approximate solution of the problem is constructed and its convergence in the corresponding function space is investigated.
Reviewer: A.Martynyuk

MSC:
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B40 Asymptotic behavior of solutions to PDEs
35A35 Theoretical approximation in context of PDEs
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References:
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