On the local existence of solutions of equations with memory not solvable with respect to the time derivative

被引：0
|
作者：
V. E. Fedorov
O. A. Stakheeva
机构：
[1] Chelyabinsk State University,
来源：
Mathematical Notes | 2015年 / 98卷
关键词：
first-order linear differential operator equation with memory; degenerate semigroup of operators; partial integro-differential equation; contraction mapping theorem; (L, p)-radial operator; pseudoparabolic equation; Banach space;
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摘要：
In this paper, on the basis of the theory of degenerate semigroups of operators and the contraction mapping theorem, we prove the local unique solvability of initial problems for a class of first-order linear differential operator equations with memory and with degenerate operator multiplying the derivative. The resulting abstract results are used to study initial boundary-value problems for partial integro-differential equations not solvable with respect to the time derivative.
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页码：472 / 483
页数：11
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