О локальной разрешимости линейных эволюционных уравнений с памятью

V. E. Fedorov; O. A. Stakheeva

Authors

V. E. Fedorov Chelyabinsk State University
O. A. Stakheeva Chelyabinsk State University

Keywords:

evolutionary equation, integro-differential equation, equation with memory, sectorial operator, analytic semigroup of operators

Abstract

The authors prove the local unique solvability of the Cauchy problem for linear evolutionary equation with sectorial operator and with integral memory operator in the Banach space. The result is illustrated on the example of the initial boundary value problem for integro-differential equation with partial derivatives.

Author Biographies

V. E. Fedorov, Chelyabinsk State University

Department of Mathematical Analysis

O. A. Stakheeva, Chelyabinsk State University

Department of Mathematical Analysis

References

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Grasselli, M. Uniform attractors of nonautonomous dynamical systems with memory / M. Grasselli, V. Pata. - In the book: Progress in nonlinear differential equations and their applications. Basel: Birkh'auser Verlag, 2002. - Vol. 50. - P. 155 - 178.