Classes of uniqueness for integrodifferential equations with volterra operators of convolution type

1979 ◽  
Vol 13 (2) ◽  
pp. 143-144 ◽  
Author(s):  
A. S. Kalashnikov
Keyword(s):  
Integrodifferential Equations ◽  
Convolution Type ◽  
Volterra Operators

scholarly journals On the Complex Inversion Formula and Admissibility for a Class of Volterra Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Ahmed Fadili ◽  
Hamid Bounit
Keyword(s):  
Inversion Formula ◽  
Evolution Equations ◽  
Point Of View ◽  
Integrodifferential Equations ◽  
Convolution Type ◽  
Martingale Differences ◽  
Volterra Systems ◽  
The Laplace Transform ◽  
Necessary And Sufficient ◽  
Resolvent Families

This paper studies Volterra integral evolution equations of convolution type from the point of view of complex inversion formula and the admissibility in the Salamon-Weiss sens. We first present results on the validity of the inverse formula of the Laplace transform for the resolvent families associated with scalar Volterra integral equations of convolution type in Banach spaces, which extends and improves the results in Hille and Philllips (1957) and Cioranescu and Lizama (2003, Lemma 5), respectively, including the stronger version for a class of scalar Volterra integrodifferential equations of convolution type on unconditional martingale differences UMD spaces, provided that the leading operator generates aC0-semigroup. Next, a necessary and sufficient condition forLp-admissibilityp∈1,∞of the system's control operator is given in terms of the UMD-property of its underlying control space for a wider class of Volterra integrodifferential equations when the leading operator is not necessarily a generator, which provides a generalization of a result known to hold for the standard Cauchy problem (Bounit et al., 2010, Proposition 3.2).

Generalized Volterra operators on polynomially generated Banach spaces

2020 ◽  
Vol Accepted ◽  
Author(s):  
Nasrin Eghbali ◽  
Maryam M. Pirasteh ◽  
Amir H. Sanatpour
Keyword(s):  
Banach Spaces ◽  
Volterra Operators

DAE-based solution of nonlinear multiterm fractional integrodifferential equations

2008 ◽  
Vol 42 (6-8) ◽  
pp. 677-688 ◽  
Author(s):  
Satwinder Jit Singh ◽  
Anindya Chatterjee
Keyword(s):  
Integrodifferential Equations

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 A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels

2021 ◽  
Vol 47 (3) ◽  
Author(s):  
Timon S. Gutleb
Keyword(s):  
Open Source ◽  
Spectral Method ◽  
Jacobi Polynomial ◽  
Numerical Experiments ◽  
Exponential Convergence ◽  
Analytic Solutions ◽  
Convolution Type ◽  
Volterra Equations ◽  
Polynomial Bases ◽  
Sparsity Structure

AbstractWe present a sparse spectral method for nonlinear integro-differential Volterra equations based on the Volterra operator’s banded sparsity structure when acting on specific Jacobi polynomial bases. The method is not restricted to convolution-type kernels of the form K(x, y) = K(x − y) but instead works for general kernels at competitive speeds and with exponential convergence. We provide various numerical experiments based on an open-source implementation for problems with and without known analytic solutions and comparisons with other methods.

scholarly journals The Calderón–Zygmund Theorem with an $$L^1$$ Mean Hörmander Condition

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Soichiro Suzuki
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Acta Math ◽  
Limited Range ◽  
Singular Integral Operators ◽  
Convolution Type ◽  
Worst Case ◽  
Hörmander Condition

AbstractIn 2019, Grafakos and Stockdale introduced an $$L^q$$ L q mean Hörmander condition and proved a “limited-range” Calderón–Zygmund theorem. Comparing their theorem with the classical one, it requires weaker assumptions and implies the $$L^p$$ L p boundedness for the “limited-range” instead of $$1< p < \infty $$ 1 < p < ∞ . However, in this paper, we show that the $$L^q$$ L q mean Hörmander condition is actually enough to obtain the $$L^p$$ L p boundedness for all $$1< p < \infty $$ 1 < p < ∞ even in the worst case $$q=1$$ q = 1 . We use a similar method to that used by Fefferman (Acta Math 124:9–36, 1970): form the Calderón–Zygmund decomposition with the bounded overlap property and approximate the bad part. Also we give a criterion of the $$L^2$$ L 2 boundedness for convolution type singular integral operators under the $$L^1$$ L 1 mean Hörmander condition.

Sign in / Sign up

Export Citation Format

Share Document