Existence and uniqueness of the solution of a Cauchy problem for the Pfaff equation with continuous coefficients

2019 ◽  
Vol 2019 (2) ◽  
pp. 18-26
Author(s):  
A. Azamov ◽  
A.O. Begaliev
Keyword(s):  
Cauchy Problem ◽  
Existence And Uniqueness ◽  
Uniqueness Of The Solution ◽  
Pfaff Equation

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.

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 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 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.

scholarly journals Fractional Operators in p -adic Variable Exponent Lebesgue Spaces and Application to p -adic Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Leonardo Fabio Chacón-Cortés ◽  
Humberto Rafeiro
Keyword(s):  
Cauchy Problem ◽  
Integral Operator ◽  
Existence And Uniqueness ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Fractional Operators ◽  
Lebesgue Spaces ◽  
Variable Exponent Lebesgue Spaces ◽  
Uniqueness Of The Solution

In this paper, we prove the boundedness of the fractional maximal and the fractional integral operator in the p -adic variable exponent Lebesgue spaces. As an application, we show the existence and uniqueness of the solution for a nonhomogeneous Cauchy problem in the p -adic variable exponent Lebesgue spaces.

ON SOME CHARACTERISTIC CAUCHY PROBLEMS

2021 ◽  
Vol 10 (8) ◽  
pp. 3055-3062
Author(s):  
Jean-André Marti
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Existence And Uniqueness ◽  
Characteristic Curve ◽  
Cauchy Problems ◽  
Uniqueness Of The Solution ◽  
Ill Posed

By means of some regularizations for an ill posed Cauchy problem, we define an associated generalized problem and discuss the conditions for solvability of it. To illustrate this, starting from the semilinear unidirectional wave equation with data given on a characteristic curve, we show existence and uniqueness of the solution in convenient generalized algebras.

Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

2002 ◽  
Vol 7 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Mifodijus Sapagovas
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Numerical Algorithms ◽  
Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

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