Asymptotic behaviour of contraction non-autonomous semi-flows in a Banach space: Application to first-order hyperbolic PDEs

Automatica ◽  
2016 ◽  
Vol 65 ◽  
pp. 140-146 ◽  
Author(s):  
Ilyasse Aksikas
Keyword(s):  
Banach Space ◽  
Asymptotic Behaviour ◽  
Space Application ◽  
Hyperbolic Pdes ◽  
First Order

Entropy numbers of embedding maps between Besov spaces with an application to eigenvalue problems

1981 ◽  
Vol 90 (1-2) ◽  
pp. 63-70 ◽  
Author(s):  
Bernd Carl
Keyword(s):  
Banach Space ◽  
Asymptotic Behaviour ◽  
Besov Spaces ◽  
Eigenvalue Problems ◽  
Function Spaces ◽  
Sequence Spaces ◽  
Entropy Numbers ◽  
Diagonal Operators

SynopsisIn this paper we determine the asymptotic behaviour of entropy numbers of embedding maps between Besov sequence spaces and Besov function spaces. The results extend those of M. Š. Birman, M. Z. Solomjak and H. Triebel originally formulated in the language of ε-entropy. It turns out that the characterization of embedding maps between Besov spaces by entropy numbers can be reduced to the characterization of certain diagonal operators by their entropy numbers.Finally, the entropy numbers are applied to the study of eigenvalues of operators acting on a Banach space which admit a factorization through embedding maps between Besov spaces.The statements of this paper are obtained by results recently proved elsewhere by the author.

Backstepping Boundary Control for First-Order Hyperbolic PDEs on Inverted Pendulum Stabilization with Constant Input Delay

2021 ◽  
Author(s):  
Arnab Pal ◽  
Ramashis Banerjee ◽  
Debottam Mukherjee ◽  
Samrat Chakraborty ◽  
Pabitra Kumar Guchhait ◽  
...  
Keyword(s):  
Boundary Control ◽  
Inverted Pendulum ◽  
Input Delay ◽  
Constant Input ◽  
Hyperbolic Pdes ◽  
First Order

scholarly journals Local Convergence for Multi-Step High Order Solvers under Weak Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 179
Author(s):  
Ramandeep Behl ◽  
Ioannis K. Argyros
Keyword(s):  
Banach Space ◽  
Nonlinear Equations ◽  
Local Convergence ◽  
Nonlinear Problems ◽  
Fréchet Derivative ◽  
High Order ◽  
Order Derivative ◽  
First Order ◽  
Lipschitz Constants ◽  
Convergence Study

Our aim in this article is to suggest an extended local convergence study for a class of multi-step solvers for nonlinear equations valued in a Banach space. In comparison to previous studies, where they adopt hypotheses up to 7th Fŕechet-derivative, we restrict the hypotheses to only first-order derivative of considered operators and Lipschitz constants. Hence, we enlarge the suitability region of these solvers along with computable radii of convergence. In the end of this study, we choose a variety of numerical problems which illustrate that our works are applicable but not earlier to solve nonlinear problems.

On solutions of a stochastic integral equation of the volterra type with applications for chemotherapy

1988 ◽  
Vol 25 (02) ◽  
pp. 257-267 ◽  
Author(s):  
D. Szynal ◽  
S. Wedrychowicz
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Stochastic Model ◽  
Asymptotic Behaviour ◽  
Existence Of Solutions ◽  
Stochastic Integral ◽  
Volterra Type ◽  
Stochastic Integral Equation

This paper deals with the existence of solutions of a stochastic integral equation of the Volterra type and their asymptotic behaviour. Investigations of this paper use the concept of a measure of non-compactness in Banach space and fixed-point theorem of Darbo type. An application to a stochastic model for chemotherapy is also presented.

scholarly journals On first-order differential operators with Bohr-Neugebauer type property

1989 ◽  
Vol 12 (3) ◽  
pp. 473-476 ◽  
Author(s):  
Aribindi Satyanarayan Rao
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Linear Operator ◽  
Real Line ◽  
Differential Operators ◽  
Bounded Solution ◽  
Almost Periodic ◽  
Bounded Linear ◽  
First Order ◽  
Type Property

We consider a differential equationddtu(t)-Bu(t)=f(t), where the functions u and f map the real line into a Banach space X and B: X→X is a bounded linear operator. Assuming that any Stepanov-bounded solution u is Stepanov almost-periodic when f is Bochner almost-periodic, we establish that any Stepanov-bounded solution u is Bochner almost-periodic when f is Stepanov almost-periodic. Some examples are given in which the operatorddt-B is shown to satisfy our assumption.

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