Passage to the limit in quasilinear integro-differential equations with weakly convergent coefficients (Q5954372)

The author studies the convergence of solutions \({u^m}(t,x)\) of the initial-boundary value problem in the rectangle for the sequence of integro-differential equations to the solution \(u^{\infty}(t,x)\) of the ``limit'' problem. Necessary and sufficient conditions are established for the validity of the passage to the ``limit'' in a sequence of integro-differential equations with weakly convergent coefficients describing physical processes in highly inhomogeneous materials with memory.