Spectral Analysis and Representations of Solutions of Abstract Integro-differential Equations in Hilbert Space

2013 ◽  
pp. 517-535 ◽  
Author(s):  
Victor V. Vlasov ◽  
Nadezda A. Rautian
Keyword(s):  
Hilbert Space ◽  
Spectral Analysis ◽  
Differential Equations

scholarly journals Correct solvability and representation of the solutions of Volterra integro-differential equations with exponential-fractional kernels

2019 ◽  
Vol 488 (5) ◽  
pp. 476-480
Author(s):  
V. V. Vlasov ◽  
N. A. Rautian
Keyword(s):  
Hilbert Space ◽  
Spectral Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Unbounded Operator ◽  
Strong Solutions ◽  
Abstract Form ◽  
Partial Differential ◽  
Operator Functions ◽  
Well Posed

For abstract integro-differential equations with unbounded operator coefficients in a Hilbert space, we study the well-posed solvability of initial problems and carry out spectral analysis of the operator functions that are symbols of these equations. This allows us to represent the strong solutions of these equations as series in exponentials corresponding to points of the spectrum of operator functions. The equations under study are the abstract form of linear integro-partial differential equations arising in viscoelasticity and several other important applications.

Global attracting sets of neutral stochastic functional integro-differential equations driven by a fractional Brownian motion

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
A. Bakka ◽  
S. Hajji ◽  
D. Kiouach
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Hurst Parameter ◽  
Fixed Point Principle ◽  
Stochastic Functional

Abstract By means of the Banach fixed point principle, we establish some sufficient conditions ensuring the existence of the global attracting sets of neutral stochastic functional integrodifferential equations with finite delay driven by a fractional Brownian motion (fBm) with Hurst parameter H ∈ ( 1 2 , 1 ) {H\in(\frac{1}{2},1)} in a Hilbert space.

scholarly journals Differential Games for an Infinite 2-Systems of Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1467
Author(s):  
Muminjon Tukhtasinov ◽  
Gafurjan Ibragimov ◽  
Sarvinoz Kuchkarova ◽  
Risman Mat Hasim
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Differential Games ◽  
Differential Game ◽  
Infinite System ◽  
The State ◽  
Geometric Constraints ◽  
Control Parameters ◽  
Systems Of Differential Equations ◽  
Pursuit And Evasion

A pursuit differential game described by an infinite system of 2-systems is studied in Hilbert space l2. Geometric constraints are imposed on control parameters of pursuer and evader. The purpose of pursuer is to bring the state of the system to the origin of the Hilbert space l2 and the evader tries to prevent this. Differential game is completed if the state of the system reaches the origin of l2. The problem is to find a guaranteed pursuit and evasion times. We give an equation for the guaranteed pursuit time and propose an explicit strategy for the pursuer. Additionally, a guaranteed evasion time is found.

scholarly journals ON SEMI-LINEAR SECOND ORDER VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS IN HILBERT SPACE

2008 ◽  
Vol 12 (3) ◽  
pp. 679-701 ◽  
Author(s):  
Jin-soo Hwang ◽  
Shin-ichi Nakagiri
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Second Order
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