Correct Solvability and Spectral Analysis of Volterra Integrodifferential Equations with Singular Kernels

2018 ◽  
Vol 482 (6) ◽  
pp. 635-638
Author(s):  
V. Vlasov ◽  
◽  
N. Rautian ◽  
Keyword(s):  
Spectral Analysis ◽  
Integrodifferential Equations ◽  
Correct Solvability ◽  
Singular Kernels

scholarly journals Investigation of Operator Models Arising in Viscoelasticity Theory

2018 ◽  
Vol 64 (1) ◽  
pp. 60-73
Author(s):  
V V Vlasov ◽  
N A Rautian
Keyword(s):  
Hilbert Space ◽  
Spectral Analysis ◽  
Unbounded Operator ◽  
Integrodifferential Equations ◽  
Abstract Form ◽  
Partial Derivatives ◽  
Correct Solvability ◽  
Operator Functions

We study the correct solvability of initial problems for abstract integrodifferential equations with unbounded operator coefficients in a Hilbert space. We do spectral analysis of operator-functions that are symbols of such equations. The equations under consideration are an abstract form of linear integrodifferential equations with partial derivatives arising in viscoelasticity theory and having a number of other important applications. We describe localization and structure of the spectrum of operatorfunctions that are symbols of such equations.

scholarly journals Asymptotics of integrodifferential models with integrable kernels II

2003 ◽  
Vol 2003 (50) ◽  
pp. 3153-3169
Author(s):  
Angelina M. Bijura
Keyword(s):  
Singular Perturbation ◽  
Mellin Transform ◽  
Perturbation Methods ◽  
Fractional Integration ◽  
Integrodifferential Equations ◽  
Singularly Perturbed ◽  
Weakly Singular Kernels ◽  
Weakly Singular ◽  
Singular Perturbation Methods ◽  
Singular Kernels

Nonlinear singularly perturbed Volterra integrodifferential equations with weakly singular kernels are investigated using singular perturbation methods, the Mellin transform technique, and the theory of fractional integration.

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