Geodesic
On the Local Existence of Solutions of Equations with Memory not Solvable with Respect to the Time Derivative
Matematičeskie zametki, Tome 98 (2015) no. 3, pp. 414-426

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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, Banach space.
Mots-clés : pseudoparabolic equation 
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     author = {V. E. Fedorov and O. A. Stakheeva},
     title = {On the {Local} {Existence} of {Solutions} of {Equations} with {Memory} not {Solvable} with {Respect} to the {Time} {Derivative}},
     journal = {Matemati\v{c}eskie zametki},
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V. E. Fedorov; O. A. Stakheeva. On the Local Existence of Solutions of Equations with Memory not Solvable with Respect to the Time Derivative. Matematičeskie zametki, Tome 98 (2015) no. 3, pp. 414-426. http://geodesic.mathdoc.fr/item/MZM_2015_98_3_a9/