|
This article is cited in 2 scientific papers (total in 2 papers)
On the Local Existence of Solutions of Equations with Memory not Solvable with Respect to the Time Derivative
V. E. Fedorov, O. A. Stakheeva Chelyabinsk State University
Abstract:
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.
Keywords:
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.
Received: 16.08.2012
Citation:
V. E. Fedorov, O. A. Stakheeva, “On the Local Existence of Solutions of Equations with Memory not Solvable with Respect to the Time Derivative”, Mat. Zametki, 98:3 (2015), 414–426; Math. Notes, 98:3 (2015), 472–483
Linking options:
https://www.mathnet.ru/eng/mzm10102https://doi.org/10.4213/mzm10102 https://www.mathnet.ru/eng/mzm/v98/i3/p414
|
Statistics & downloads: |
Abstract page: | 337 | Full-text PDF : | 136 | References: | 44 | First page: | 38 |
|