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.

scholarly journals Existence of solutions of nonlinear integrodifferential equation with nonlocal condition

1997 ◽  
Vol 10 (3) ◽  
pp. 279-288 ◽  
Author(s):  
K. Balachandran ◽  
M. Chandrasekaran
Keyword(s):  
Cauchy Problem ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Nonlocal Condition ◽  
Global Solutions ◽  
Contraction Mapping Principle ◽  
Local And Global Solutions ◽  
Nonlocal Cauchy Problem

In this paper we prove the existence and uniqueness of local and global solutions of a nonlocal Cauchy problem for a class of integrodifferential equation. The method of semigroups and the contraction mapping principle are used to establish the results.

scholarly journals Asymptotic Behavior of Solutions to Abstract Stochastic Fractional Partial Integrodifferential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhi-Han Zhao ◽  
Yong-Kui Chang ◽  
Juan J. Nieto
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Integrodifferential Equation ◽  
Fixed Point Theorems ◽  
Mild Solutions ◽  
Integrodifferential Equations ◽  
Linear Operators ◽  
Asymptotic Behavior Of Solutions ◽  
Almost Automorphic ◽  
Partial Integrodifferential Equation

The existence of asymptotically almost automorphic mild solutions to an abstract stochastic fractional partial integrodifferential equation is considered. The main tools are some suitable composition results for asymptotically almost automorphic processes, the theory of sectorial linear operators, and classical fixed point theorems. An example is also given to illustrate the main theorems.

scholarly journals Space ofω-Periodic Limit Functions and Its Applications to an Abstract Cauchy Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Rui Xie ◽  
Chuanyi Zhang
Keyword(s):  
Cauchy Problem ◽  
Function Space ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Abstract Cauchy Problem ◽  
Type Function ◽  
Inclusion Relations ◽  
Asymptotically Periodic ◽  
New Space ◽  
Study Inclusion

We introduce a new space consisting of what we callω-periodic limit functions. We investigate some properties of the new function space. In particular, we study inclusion relations among asymptotically periodic type function spaces. Finally, we apply theω-periodic limit functions to investigate the existence and uniqueness of asymptoticallyω-periodic mild solutions of an abstract Cauchy problem.

scholarly journals Nonlocal Cauchy problem for nonlinear mixed integrodifferential equations

2010 ◽  
Vol 41 (4) ◽  
pp. 361-374
Author(s):  
H. L. Tidke ◽  
M. B. Dhakne
Keyword(s):  
Cauchy Problem ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Strong Solutions ◽  
Integrodifferential Equations ◽  
Nonlocal Cauchy Problem

The present paper investigates the existence and uniqueness of mild and strong solutions of a nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition. The results obtained by using Schauder fixed point theorem and the theory of semigroups.

On mild solutions of gradient systems in Hilbert spaces

2013 ◽  
Vol 11 (11) ◽  
Author(s):  
Andrzej Rozkosz
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Backward Stochastic Differential Equations ◽  
Stochastic Representation ◽  
Infinite Dimensional ◽  
The Cauchy Problem

AbstractWe consider the Cauchy problem for an infinite-dimensional Ornstein-Uhlenbeck equation perturbed by gradient of a potential. We prove some results on existence and uniqueness of mild solutions of the problem. We also provide stochastic representation of mild solutions in terms of linear backward stochastic differential equations determined by the Ornstein-Uhlenbeck operator and the potential.

scholarly journals THE NON-LOCAL CAUCHY PROBLEM FOR SEMILINEAR INTEGRODIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENT

2001 ◽  
Vol 44 (1) ◽  
pp. 63-70 ◽  
Author(s):  
K. Balachandran ◽  
M. Chandrasekaran
Keyword(s):  
Cauchy Problem ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Subject Classification ◽  
Classical Solutions ◽  
Deviating Argument ◽  
Primary 34K05 ◽  
Non Local

AbstractThe aim of this paper is to prove the existence and uniqueness of mild and classical solutions of the non-local Cauchy problem for a semilinear integrodifferential equation with deviating argument. The results are established by using the method of semigroups and the contraction mapping principle. The paper generalizes certain results of Lin and Liu.AMS 2000 Mathematics subject classification: Primary 34K05; 34K30

scholarly journals Semilinear Volterra Integrodifferential Problems with Fractional Derivatives in the Nonlinearities

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Mokhtar Kirane ◽  
Milan Medveď ◽  
Nasser-eddine Tatar
Keyword(s):  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Mild Solutions ◽  
Second Order ◽  
Classical Solutions ◽  
Volterra Integrodifferential Equation

A second-order semilinear Volterra integrodifferential equation involving fractional time derivatives is considered. We prove existence and uniqueness of mild solutions and classical solutions in appropriate spaces.

scholarly journals Existence and Uniqueness of Fuzzy Control Integro-Differential Equation with Perturbed

2013 ◽  
Vol 3 ◽  
pp. 37-44 ◽  
Author(s):  
N. Phuong ◽  
N.N. Phung ◽  
H. Vu
Keyword(s):  
Differential Equation ◽  
Fuzzy Control ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Integro Differential Equation

In the paper, we discuss the existence and uniqueness solution of fuzzy control integrodifferential equation with perturbed. The method of successive approximations is utilized toestablish these results.

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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