scholarly journals Existence, uniqueness and monotonic behavior of the solution of classical flow distribution problem for hydraulic networks with pressure-dependent closure relations

2019 ◽  
Vol 102 ◽  
pp. 01004 ◽  
Author(s):  
Leonid Korelstein
Keyword(s):  
Existence And Uniqueness ◽  
Flow Distribution ◽  
Uniqueness Of Solution ◽  
Distribution Problem ◽  
Closure Relation ◽  
Closure Relations ◽  
Monotonicity Conditions ◽  
Hydraulic Networks

Existence, uniqueness and monotonic behavior of the solution of classical flow distribution problem for hydraulic networks with pressure-dependent closure relations was proved. The closure relation can have very general form, restricted only by continuity and monotonicity conditions necessary for providing existence, uniqueness and continuity of flow distribution problem for each branch. It is shown that network as a whole “inherits” monotonicity and continuity of its branches behavior, and this provides existence and uniqueness of solution.

scholarly journals Hydraulic networks with pressure-dependent closure relations, under restrictions on the value of nodal pressures. Maxwell matrix properties and monotonicity of flow distribution problem solution

2019 ◽  
Vol 102 ◽  
pp. 01005 ◽  
Author(s):  
Leonid Korelstein
Keyword(s):  
Existence Theorems ◽  
Flow Distribution ◽  
Previous Article ◽  
Problem Solution ◽  
Distribution Problem ◽  
Matrix Properties ◽  
Hydraulic Network ◽  
Closure Relations ◽  
Hydraulic Networks

In the article, which continues the research of article [1], the results of previous article are generalized to “abstract” hydraulic networks. Additional existence theorems are proved for classical flow distribution problem (CFDP) for hydraulic networks with pressure-dependent closure relations, under restriction on nodal pressures. Hydraulic network Maxwell matrix properties are establish, related to monotonicity of CFDP solution.

Fuzzy double controlled metric spaces and related results

2021 ◽  
Vol 40 (5) ◽  
pp. 9977-9985
Author(s):  
Naeem Saleem ◽  
Hüseyin Işık ◽  
Salman Furqan ◽  
Choonkil Park
Keyword(s):  
Integral Equation ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Uniqueness Of Solution ◽  
Contraction Principle ◽  
Triangular Inequality ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we introduce the concept of fuzzy double controlled metric space that can be regarded as the generalization of fuzzy b-metric space, extended fuzzy b-metric space and controlled fuzzy metric space. We use two non-comparable functions α and β in the triangular inequality as: M q ( x , z , t α ( x , y ) + s β ( y , z ) ) ≥ M q ( x , y , t ) ∗ M q ( y , z , s ) . We prove Banach contraction principle in fuzzy double controlled metric space and generalize the Banach contraction principle in aforementioned spaces. We give some examples to support our main results. An application to existence and uniqueness of solution for an integral equation is also presented in this work.

scholarly journals On the existence and uniqueness of solution to Volterra equation on a time scale

2019 ◽  
Vol 27 (3) ◽  
pp. 177-194
Author(s):  
Bartłomiej Kluczyński
Keyword(s):  
Integral Equation ◽  
Sobolev Space ◽  
Time Scale ◽  
Existence And Uniqueness ◽  
Nonlinear Term ◽  
Volterra Equation ◽  
Uniqueness Of Solution ◽  
Inversion Theorem ◽  
T Tau

AbstractUsing a global inversion theorem we investigate properties of the following operator\matrix{\matrix{ V(x)( \cdot ): = {x^\Delta }( \cdot ) + \int_0^ \cdot {v\left( { \cdot ,\tau ,x,\left( \tau \right)} \right)} \Delta \tau , \hfill \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x(0) = 0, \hfill \cr}\cr {} \cr }in a time scale setting. Under some assumptions on the nonlinear term v we then show that there exists exactly one solution {x_y} \in W_{\Delta ,0}^{1,p}\left( {{{[0,1]}_\mathbb{T}},{\mathbb{R}^N}} \right) to the associated integral equation\left\{ {\matrix{{{x^\Delta }(t) + \int_0^t {v\left( {t,\tau ,x\left( \tau \right)} \right)} \Delta \tau = y(t)\,\,\,for\,\Delta - a.e.\,\,\,t \in {{[0.1]}_\mathbb{T}},} \cr {x(0) = 0,} \cr } } \right.which is considered on a suitable Sobolev space.

scholarly journals On solvability of nonlinear integro-differential equation

2020 ◽  
pp. 127-134
Author(s):  
А.В. Юлдашева
Keyword(s):  
Differential Equation ◽  
Existence And Uniqueness ◽  
Initial Problem ◽  
Uniqueness Of Solution ◽  
Integro Differential Equation ◽  
Peridynamic Model

В настоящей работе рассматривается задача с начальными данными для нелинейного интегро-дифференциального уравнения, связанного с перидинамической моделью. Доказывается существование и единственность решения. In this paper we consider initial problem for nonlinear integro-differential equation related to peridynamic model. The existence and uniqueness of solution are proved.

scholarly journals Existence and uniqueness of the solution for Lobacevsky’s functional equation

2002 ◽  
pp. 66-70
Author(s):  
Nicolae Neamtu
Keyword(s):  
Functional Equation ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solution ◽  
Uniqueness Of The Solution

The purpose of this paper is to give a theorem for the existence and uniqueness of solution of Lobacevsky's functional equation and to effective find it.

On the Existence and Uniqueness of Solution of MRE and Applications

2017 ◽  
Vol 19 (4) ◽  
pp. 1241-1250 ◽  
Author(s):  
Yunhui Hou ◽  
Nikolaos Limnios ◽  
Walter Schön
Keyword(s):  
Existence And Uniqueness ◽  
Uniqueness Of Solution
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