Existence of entropy solutions for some nonlinear elliptic problems involving variable exponent and measure data

Ahmedatt, Taghi; Azroul, Elhoussine; Hjiaj, Hassane; Touzani, Abdelfattah

doi:10.5269/bspm.v36i2.30581

Cited by 6 publications

(10 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is necessary to emphasize the attention on the point that from the position of the theory of information it represents the eliminated uncertainty of behavior of the system and is numerically equal to the reduction of this uncertainty. Let in the initial state the banking system was in a chaotic state with a maximum entropy (Н m ), then the amount of the seized information would be determined as follows [15]:…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Entropy-Informational Approach to Analysis of Self-Ogranization of Banking System

Tkachuk¹

2019

EUREKA: Social and Humanities

View full text Add to dashboard Cite

The evolving economy today is non-stationary in the nature of its character of behavior which becomes the reason of emergence of imbalances and instability of the market environment that cause the emergence of nonlinear processes in functioning of the banking system which may carry a threat to its development. Super fast tempos of change in the globalized world generate flows of institutional and innovative disturbances that test banks and banking systems for viability and encourage them to study the peculiarities of their behavior in terms of non-linearity and non-equilibrium. Knowledge and interpretation of synergetic properties of the banking system today have not only theoretical but also practical significance for development and implementation of the concept of self-organization of banks. The theoretical questions of mutual influence and interconnection of entropy and information on the processes of self-organization in the banking system are considered. The functioning of the banking system in an unstable environment with chaotic and orderly behavioral stages is characterized by a nonlinear dynamics of entropy, as well as a significant dependence on the influence of management information that enters the system. Saturation of the banking system with this information makes it possible to force out chaos from it, it increases its orderliness and effect of functioning. From the point of view of entropy and informational approach, the nature and conditions of self-organization in the banking system are disclosed. It was established, that fundamental condition for self-organization in the banking system is to transfer the system to a non-equilibrium state when it becomes quite sensitive to external disturbances. It is noted, that entropy represents a measure of disorder of the system, and its growth increases chaos and can lead to devastating consequences in the functioning of the system. The processes of self-organization in the banking system will only be possible if its order is growing.

show abstract

Section: Resultsmentioning

confidence: 99%

“…where I is the number of the seized information; H m is the maximum possible entropy of the source of information; H is entropy of the source of information; Then, formula (1) can be represented as follows [12,15]:…”

Section: Resultsmentioning

confidence: 99%

Entropy-Informational Approach to Analysis of Self-Ogranization of Banking System

Tkachuk¹

2019

EUREKA: Social and Humanities

View full text Add to dashboard Cite

show abstract

“…where N is entropy of the source of information; H m is the maximum possible entropy of the source of information; R is the level of orderliness (relative entropy). Analyzing the above formula 1, it is quite obvious, that the magnitude of the index of degree of orderliness (relative entropy) (R) is in the range from 0 to 1, therefore its boundary values (R=0) correspond to the missing order in the system and characterize the degree of entropy, or show a perfect order when R=1, and the entropy level is equal to 0 [9].…”

Section: Resultsmentioning

confidence: 99%

“…For example, when the system's behavior becomes disorderly and threatens its integrity, the desire to curb and suspend the further entropy of functioning of the banking system by increasing the influence of the governing bodies through the use of their regulatory and managerial information is quite natural and obvious. Just in this the synergistic principle of I. Prigozhyna finds its reflection, when from the chaos in the system the order is formed, and evolving system undergoes restructuring and goes into a qualitatively new state [4,9]. Similar considerations are given for the right-hand part of the inequality (4).…”

Section: Economics Econometrics and Financementioning

confidence: 99%

Entropy Conditions of Self-Organization of the Banking System

Tkachuk

Buchkovskaya

2019

Technology transfer: innovative solutions in Social Sciences an

View full text Add to dashboard Cite

The conditions for market transformations are accompanied by a growing influence on the banks' activity by the flow of destructive disturbances that can cause chaotic behavior of the economic system as a whole and the banking system, in particular. The purpose of the study is to identify the preface of self-organization of the banking system, taking into account the information factor and the level of the entropy of the system. The theoretical questions of mutual influence and interconnection of entropy and information are considered in the paper, as well as their influence on the processes of self-organization in the banking system. From the point of view of the entropy approach the nature and conditions of self-organization in the banking system are disclosed. For the efficient functioning of the modern banking system, the search and analysis of the dependence between the entropy indicators, accumulated information and the synergistic effect, taking into account dualism of chaos and order, are of considerable interest. On the basis of the complex of these indicators, the results of the conducted research, which reveal the dynamic properties of self-organization of the banking system, are presented.

show abstract

“…For the anisotropic case such representation is not known. The existence of entropy solutions of the Dirichlet problem in bounded domains Ω for equations with variable exponent nonlinearities of the type (1.1) was studied in [29], [30], [31], [32]. Namely, it was proved in [29], [30] that for µ ∈ L 1 (Ω) there exists an entropy solution of the equation (1.1) under homogeneous boundary conditions u| ∂Ω = 0.…”

Section: Let Us Denotementioning

confidence: 99%

On solutions of anisotropic elliptic equations with variable exponent and measure data

Kozhevnikova

2019

Complex Variables and Elliptic Equations

View full text Add to dashboard Cite

Anisotropic elliptic equations of the second order with variable exponents in nonlinearities and the right-hand side as a diffuse measure are considered in the space R n . The existence of an entropy solution in anisotropic Sobolev-Orlicz spaces with variable exponents is proved. The obtained entropy solution is shown to be a renormalized solution. (2000). Primary 35J62; Secondary 35J25. Mathematics Subject Classification

show abstract

Existence of entropy solutions for some nonlinear elliptic problems involving variable exponent and measure data

Cited by 6 publications

References 12 publications

Entropy-Informational Approach to Analysis of Self-Ogranization of Banking System

Entropy-Informational Approach to Analysis of Self-Ogranization of Banking System

Entropy Conditions of Self-Organization of the Banking System

On solutions of anisotropic elliptic equations with variable exponent and measure data

Contact Info

Product

Resources

About