scholarly journals Cauchy problem for a system of equations with the partial Gerasimov – Caputo derivatives

2021 ◽  
Vol 21 (4) ◽  
pp. 22-29
Author(s):  
M.O. Mamchuev ◽  
Keyword(s):  
Cauchy Problem ◽  
Existence And Uniqueness ◽  
Rectangular Domain ◽  
System Of Equations ◽  
General Representation ◽  
Caputo Derivatives ◽  
Uniqueness Of The Solution

For the system of equations with the partial Gerasimov – Caputo derivatives, a general representation of regular in a rectangular domain solutions is constructed. Cauchy problem is investigated. Theorems of existence and uniqueness of the solution are proved.

scholarly journals ON STOCHASTIC GENERALIZED FUNCTIONS

2011 ◽  
Vol 14 (02) ◽  
pp. 237-260 ◽  
Author(s):  
PEDRO CATUOGNO ◽  
CHRISTIAN OLIVERA
Keyword(s):  
Cauchy Problem ◽  
Existence And Uniqueness ◽  
Generalized Functions ◽  
Uniqueness Of The Solution ◽  
Stochastic Cauchy Problem

In this work we introduce a new algebra of stochastic generalized functions. The regular Hida distributions in [Formula: see text] are embedded in this algebra via their chaos expansions. As an application, we prove the existence and uniqueness of the solution of a stochastic Cauchy problem involving singularities.

Algorithm for the Calculation of the Two Variables Cubic Spline Function

2013 ◽  
Vol 59 (1) ◽  
pp. 149-161
Author(s):  
Ion Lixandru
Keyword(s):  
Existence And Uniqueness ◽  
Spline Function ◽  
Global Solutions ◽  
Cubic Spline ◽  
Practical Calculation ◽  
System Of Equations ◽  
Interpolation Spline ◽  
Linear System Of Equations ◽  
Uniqueness Of The Solution ◽  
Cubic Spline Function

Abstract When having just one variable, the existence and uniqueness of the interpolation spline function reduces to studying the solutions of an algebrical system of equations. This allows us to find a practical way of calculating the interpolation spline function. Also in the case of two variables spline functions, we can construct a linear system of equations determined by the continuity conditions of the spline function and of its partial derivatives on the edge of each division rectangle. The existence and uniqueness of the solution of the obtained system ensure the existence and uniqueness of the two variables interpolation spline function and offers a practical calculation method. This can be used to determine approximate global solutions, of some partial differential equations, solutions whose values can be determined at any point of their domain of definition and can provide information on derivatives approximate of solutions. After calculating the two variable cubic spline function, we must assess the rest of the approximation.

scholarly journals Picard and Adomian Solutions of a Nonlocal Cauchy Problem of a Delay Dierential Equation

2021 ◽  
pp. 30-43
Author(s):  
E. A. A. Ziada
Keyword(s):  
Cauchy Problem ◽  
Existence And Uniqueness ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Uniqueness Of The Solution ◽  
Picard Method ◽  
Delay Differential ◽  
Nonlocal Cauchy Problem

In this paper, two methods are used to solve a nonlocal Cauchy problem of a delay differential equation; Adomian decomposition method (ADM) and Picard method. The existence and uniqueness of the solution are proved. The convergence of the series solution and the error analysis are studied.

scholarly journals The Cauchy Problem for Parabolic Equations with Degeneration

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Ivan Pukal’skii ◽  
Bohdan Yashan
Keyword(s):  
Boundary Condition ◽  
Cauchy Problem ◽  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Arbitrary Order ◽  
Power Weight ◽  
The Cauchy Problem ◽  
Uniqueness Of The Solution ◽  
Set Of Points

Annotation. For a second-order parabolic equation, the multipoint in time Cauchy problem is considered. The coefficients of the equation and the boundary condition have power singularities of arbitrary order in time and space variables on a certain set of points. Conditions for the existence and uniqueness of the solution of the problem in Hölder spaces with power weight are found.

scholarly journals On the weighted boundary value problem for systems of degenerate ordinary differential equations

2010 ◽  
Vol 51 ◽  
Author(s):  
Stasys Rutkauskas ◽  
Igor Saburov
Keyword(s):  
Singular Point ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Linear Equations ◽  
System Of Equations ◽  
The Matrix ◽  
Uniqueness Of The Solution ◽  
Weighted Boundary ◽  
Well Posed

A system of ordinary second order linear equations with a singular point is considered. The aim of this work is such that the system of eigenvectors of the matrix that couples the system of equations is not complete. That implies a matter of the statement of a weighted boundary value problem for this system. The well-posed boundary value problem is proposed in the article. The existence and uniqueness of the solution is proved.

scholarly journals Mathematical Analysis of a Thermostatted Equation with a Discrete Real Activity Variable

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 57 ◽  
Author(s):  
Carlo Bianca ◽  
Marco Menale
Keyword(s):  
Cauchy Problem ◽  
Kinetic Theory ◽  
Stationary State ◽  
Mathematical Analysis ◽  
Existence And Uniqueness ◽  
Real Activity ◽  
Uniqueness Of The Solution ◽  
Theory Equation ◽  
Activity Variable ◽  
Non Equilibrium

This paper deals with the mathematical analysis of a thermostatted kinetic theory equation. Specifically, the assumption on the domain of the activity variable is relaxed allowing for the discrete activity to attain real values. The existence and uniqueness of the solution of the related Cauchy problem and of the related non-equilibrium stationary state are established, generalizing the existing results.

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