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 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 A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional response

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Assane Savadogo ◽  
Boureima Sangaré ◽  
Hamidou Ouedraogo
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Functional Response ◽  
Mathematical Analysis ◽  
Existence And Uniqueness ◽  
Nonlinear Functional ◽  
Uniqueness Of The Solution ◽  
Nontrivial Periodic Solutions ◽  
Predator Model ◽  
Stability Results

AbstractIn this paper, our aim is mathematical analysis and numerical simulation of a prey-predator model to describe the effect of predation between prey and predator with nonlinear functional response. First, we develop results concerning the boundedness, the existence and uniqueness of the solution. Furthermore, the Lyapunov principle and the Routh–Hurwitz criterion are applied to study respectively the local and global stability results. We also establish the Hopf-bifurcation to show the existence of a branch of nontrivial periodic solutions. Finally, numerical simulations have been accomplished to validate our analytical findings.

scholarly journals On the Cauchy Problem of Vectorial Thermostatted Kinetic Frameworks

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 517
Author(s):  
Carlo Bianca ◽  
Bruno Carbonaro ◽  
Marco Menale
Keyword(s):  
Cauchy Problem ◽  
Mathematical Analysis ◽  
Social Systems ◽  
Future Research ◽  
Research Directions ◽  
State Variable ◽  
The Cauchy Problem ◽  
Uniqueness Of The Solution ◽  
Global Existence And Uniqueness ◽  
Future Research Directions

This paper is devoted to the derivation and mathematical analysis of new thermostatted kinetic theory frameworks for the modeling of nonequilibrium complex systems composed by particles whose microscopic state includes a vectorial state variable. The mathematical analysis refers to the global existence and uniqueness of the solution of the related Cauchy problem. Specifically, the paper is divided in two parts. In the first part the thermostatted framework with a continuous vectorial variable is proposed and analyzed. The framework consists of a system of partial integro-differential equations with quadratic type nonlinearities. In the second part the thermostatted framework with a discrete vectorial variable is investigated. Real world applications, such as social systems and crowd dynamics, and future research directions are outlined in the paper.

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 Existence of Solutions of a Partial Integrodifferential Equation with Thermostat and Time Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Carlo Bianca ◽  
Luca Guerrini ◽  
Annie Lemarchand
Keyword(s):  
Cauchy Problem ◽  
Time Delay ◽  
Integrodifferential Equation ◽  
Mathematical Analysis ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Mild Solutions ◽  
Kinetic Equations ◽  
Successive Approximations ◽  
Partial Integrodifferential Equation

This paper deals with the mathematical analysis of a retarded partial integrodifferential equation that belongs to the class of thermostatted kinetic equations with time delay. Specifically, the paper is devoted to the proof of the existence and uniqueness of mild solutions of the related Cauchy problem. The main result is obtained by employing integration along the characteristic curves and successive approximations sequence arguments. Applications and perspective are also discussed within the paper.

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