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Passage to the limit in quasilinear integro-differential equations with weakly convergent coefficients. (English. Russian original) Zbl 0990.45005
Comput. Math. Math. Phys. 40, No. 3, 408-418 (2000); translation from Zh. Vychisl. Mat. Mat. Fiz. 40, No. 3, 428-439 (2000).
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.
45K05 Integro-partial differential equations
45M05 Asymptotics of solutions to integral equations
45G10 Other nonlinear integral equations
45Q05 Inverse problems for integral equations