Non‐Hermitian perturbations of Hermitian matrix‐sequences and applications to the spectral analysis of the numerical approximation of partial differential equations

2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Giovanni Barbarino ◽  
Stefano Serra‐Capizzano
Keyword(s):  
Spectral Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Approximation ◽  
Hermitian Matrix ◽  
Partial Differential

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.

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