scholarly journals On the Honesty in Nonlocal and Discrete Fragmentation Dynamics in Size and Random Position

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
S. C. Oukouomi Noutchie ◽  
E. F. Doungmo Goufo
Keyword(s):  
Initial Value Problem ◽  
Sufficient Conditions ◽  
Initial Value ◽  
Fragmentation Rate ◽  
Random Position ◽  
Fragmentation Dynamics ◽  
Substochastic Semigroups ◽  
Parameter Dependent ◽  
Fragmentation Processes ◽  
New Particles

A discrete initial-value problem describing multiple fragmentation processes, where the fragmentation rate is size and position dependent and where new particles are spatially randomly distributed according to some probabilistic law, is investigated by means of parameter-dependent operators together with the theory of substochastic semigroups with a parameter. The existence of semigroups is established for each parameter and “glued” together so as to obtain a semigroup to the full space. Under certain conditions on each fragmentation rate, we used Kato’s Theorem in to show the existence of the generator and we provide sufficient conditions for honesty.

ORDER AND CONVERGENCE OF THE ENHANCED 3-POINT FULLY IMPLICIT SUPER CLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING INITIAL VALUE PROBLEM

2021 ◽  
Vol 5 (2) ◽  
pp. 442-446
Author(s):  
Muhammad Abdullahi ◽  
Hamisu Musa
Keyword(s):  
Initial Value Problem ◽  
Initial Value Problems ◽  
Sufficient Conditions ◽  
Initial Value ◽  
Differentiation Formula ◽  
Stiff Initial Value Problems ◽  
First Order ◽  
Backward Differentiation Formula ◽  
Fully Implicit ◽  
Necessary And Sufficient

This paper studied an enhanced 3-point fully implicit super class of block backward differentiation formula for solving stiff initial value problems developed by Abdullahi & Musa and go further to established the necessary and sufficient conditions for the convergence of the method. The method is zero stable, A-stable and it is of order 5. The method is found to be suitable for solving first order stiff initial value problems

scholarly journals Some Mathematical Aspects of f(R)-Gravity with Torsion: Cauchy Problem and Junction Conditions

Universe ◽  
2019 ◽  
Vol 5 (12) ◽  
pp. 224 ◽  
Author(s):  
Stefano Vignolo
Keyword(s):  
Cauchy Problem ◽  
Initial Value Problem ◽  
Sufficient Conditions ◽  
Well Posedness ◽  
Junction Conditions ◽  
Field Equations ◽  
Initial Value ◽  
The Cauchy Problem ◽  
General Conditions

We discuss the Cauchy problem and the junction conditions within the framework of f ( R ) -gravity with torsion. We derive sufficient conditions to ensure the well-posedness of the initial value problem, as well as general conditions to join together on a given hypersurface two different solutions of the field equations. The stated results can be useful to distinguish viable from nonviable f ( R ) -models with torsion.

scholarly journals Existence and uniqueness of analytic solutions of the Shabat equation

2005 ◽  
Vol 2005 (8) ◽  
pp. 855-862 ◽  
Author(s):  
Eugenia N. Petropoulou
Keyword(s):  
Upper Bound ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Analytic Solution ◽  
Sufficient Conditions ◽  
Analytic Solutions ◽  
Initial Condition ◽  
Initial Value ◽  
First Derivative

Sufficient conditions are given so that the initial value problem for the Shabat equation has a unique analytic solution, which, together with its first derivative, converges absolutely forz∈ℂ:|z|<T,T>0. Moreover, a bound of this solution is given. The sufficient conditions involve only the initial condition, the parameters of the equation, andT. Furthermore, from these conditions, one can obtain an upper bound forT. Our results are in consistence with some recently found results.

scholarly journals Existence, uniqueness and continuability of solutions of impulsive differential-difference equations

1999 ◽  
Vol 12 (3) ◽  
pp. 293-300 ◽  
Author(s):  
D. D. Bainov ◽  
I. M. Stamova
Keyword(s):  
Difference Equations ◽  
Initial Value Problem ◽  
Sufficient Conditions ◽  
Initial Value

We consider an initial value problem for impulsive differential-difference equations, and obtain sufficient conditions for the existence, uniqueness, and continuability of solutions of such problem.

Bounded solutions of functional differential equations of the neutral type with infinite delays

1982 ◽  
Vol 93 (1-2) ◽  
pp. 33-39 ◽  
Author(s):  
V. G. Angelov ◽  
D. D. Bainov
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Bounded Solutions ◽  
Initial Value ◽  
Infinite Delays ◽  
Functional Differential

SynopsisIn this paper the authors obtain sufficient conditions for the existence and uniqueness of the initial value problem of functional differential equations of neutral type with infinite delays, making use of some earlier results of the present authors.

scholarly journals Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Josef Diblík ◽  
Josef Rebenda ◽  
Zdeněk Šmarda
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problem ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Asymptotic Formulas ◽  
Asymptotic Behavior Of Solutions ◽  
Initial Value ◽  
Singular Initial Value Problem ◽  
The Right

The paper is devoted to the study of the solvability of a singular initial value problem for systems of ordinary differential equations. The main results give sufficient conditions for the existence of solutions in the right-hand neighbourhood of a singular point. In addition, the dimension of the set of initial data generating such solutions is estimated. An asymptotic behavior of solutions is determined as well and relevant asymptotic formulas are derived. The method of functions defined implicitly and the topological method (Ważewski's method) are used in the proofs. The results generalize some previous ones on singular initial value problems for differential equations.

On a global diffeomorphism between two Banach spaces and some application

2015 ◽  
Vol 52 (1) ◽  
pp. 65-86
Author(s):  
Marek Galewski ◽  
Marcin Koniorczyk
Keyword(s):  
Critical Point ◽  
Banach Spaces ◽  
Standard Method ◽  
Initial Value Problem ◽  
Critical Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Duality Mapping ◽  
Initial Value

We provide sufficient conditions for a mapping acting between two Banach spaces to be a diffeomorphism. We get local diffeomorhism by standard method while in making it global we employ a critical point theory and a duality mapping. We provide application to integro-differential initial value problem for which we get differentiable dependence on parameters.

Necessary and sufficient conditions for existence of solutions for initial value problem of fuzzy Bagley-Torvik equation and solution representation

2021 ◽  
pp. 1-16
Author(s):  
Sunae Pak ◽  
Huichol Choe ◽  
Kinam Sin ◽  
Sunghyok Kwon
Keyword(s):  
Initial Value Problem ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Inequality Constraints ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Initial Value ◽  
Solution Representation ◽  
Necessary And Sufficient

In this paper, we investigate the necessary and sufficient conditions for existence of solutions for initial value problem of fuzzy Bagley-Torvik equation and the solution representation by using the multivariate Mittag-Leffler function. First we convert fuzzy initial value problem into the cut problem (system of fractional differential equations with inequality constraints) and obtain existence results for the solution of the cut problem under (1,1)- differentiability. Next we study the conditions for the solutions of the cut problem to constitute the solution of a fuzzy initial value problem and suggest a necessary and sufficient condition for the (1,1)-solution. Also, some examples are given to verify the effectiveness of our proposed method. The necessary and sufficient condition, solution representation for (1,2)-solution of initial value problem of fuzzy fractional Bagley-Torvik equation are shown in Appendix.

scholarly journals Lipschitz stability of impulsive functional-differential equations

2001 ◽  
Vol 42 (4) ◽  
pp. 504-514 ◽  
Author(s):  
D. D. Bainov ◽  
I. M. Stamova
Keyword(s):  
Population Dynamics ◽  
Differential Equations ◽  
Initial Value Problem ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Lipschitz Stability ◽  
Initial Value ◽  
Functional Differential

AbstractAn initial value problem is considered for impulsive functional-differential equations. The impulses occur at fixed moments of time. Sufficient conditions are found for Lipschitz stability of the zero solution of these equations. An application in impulsive population dynamics is also discussed.

scholarly journals SYNCHRONIZATION OF SWITCH DYNAMICAL SYSTEMS

2002 ◽  
Vol 12 (08) ◽  
pp. 1813-1826 ◽  
Author(s):  
MARIUS-F. DANCA
Keyword(s):  
Dynamical Systems ◽  
Differential Inclusion ◽  
Initial Value Problem ◽  
Initial Value Problems ◽  
Sufficient Conditions ◽  
Initial Value ◽  
Generalized Derivative ◽  
Filippov Regularization ◽  
Piecewise Continuous ◽  
Class Of Functions

The well known synchronization method of Fujisaka and Yamada is adapted to a particular class of piecewise continuous dynamical systems. We give sufficient conditions for the underlying initial value problems, in order to define dynamical systems. For this purpose the Filippov regularization is used, the discontinuous initial value problem being switched into a differential inclusion. A generalized derivative for the considered class of functions is introduced.

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