Inverse problem of determining the coefficient and kernel in an integro - differential equation of parabolic type

Original Problem ◽

Parabolic Type ◽

Differential Heat ◽

Inverse Boundary ◽

Fixed Point Principle ◽

This article is concerned with the study of the unique solvability of inverse boundary value problem for integro-differential heat equation. To study the solvability of the inverse problem, we first reduce the considered problem to an auxiliary system with trivial data and prove its equivalence (in a certain sense) to the original problem. Then using the Banach fixed point principle, the existence and uniqueness of a solution to this system is shown.

Existence and uniqueness of solutions for the system ofintegro-differential equations with three-point and nonlinear integral boundary conditions

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS ◽

10.31489/2020m3/26-37 ◽

2020 ◽

Vol 99 (3) ◽

pp. 23-37

Author(s):

M.J. Mardanov ◽

◽

Y.A. Sharifov ◽

K.E. Ismayilova ◽

◽

...

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Original Problem ◽

Integral Boundary Conditions ◽

Uniqueness Of Solutions ◽

Integral Boundary ◽

First Order ◽

Fixed Point Principle ◽

The paper examines a system of nonlinear integro-differential equations with three-point and nonlinear integral boundary conditions. The original problem demonstrated to be equivalent to integral equations by using Green function. Theorems on the existence and uniqueness of a solution to the boundary value problems for the first order nonlinear system of integro- differential equations with three-point and nonlinear integral boundary conditions are proved. A proof of uniqueness theorem of the solution is obtained by Banach fixed point principle, and the existence theorem then follows from Schaefer’s theorem.

Inverse boundary-value problem for the equation of longitudinal wave propagation with non-self-adjoint boundary conditions

Filomat ◽

10.2298/fil1916259a ◽

2019 ◽

Vol 33 (16) ◽

pp. 5259-5271

Author(s):

Elvin Azizbayov ◽

Yashar Mehraliyev

Keyword(s):

Inverse Problem ◽

Wave Propagation ◽

Boundary Value Problem ◽

Boundary Conditions ◽

Longitudinal Wave ◽

Original Problem ◽

Boundary Value ◽

Inverse Boundary ◽

Longitudinal Wave Propagation

We study the inverse coefficient problem for the equation of longitudinal wave propagation with non-self-adjoint boundary conditions. The main purpose of this paper is to prove the existence and uniqueness of the classical solutions of an inverse boundary-value problem. To investigate the solvability of the inverse problem, we carried out a transformation from the original problem to some equivalent auxiliary problem with trivial boundary conditions. Applying the Fourier method and contraction mappings principle, the solvability of the appropriate auxiliary inverse problem is proved. Furthermore, using the equivalency, the existence and uniqueness of the classical solution of the original problem are shown.

On a Fractional SPDE Driven by Fractional Noise and a Pure Jump Lévy Noise inℝd

Abstract and Applied Analysis ◽

10.1155/2014/758270 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Xichao Sun ◽

Zhi Wang ◽

Jing Cui

Keyword(s):

Differential Equation ◽

Partial Differential Equation ◽

Fixed Point ◽

Stochastic Partial Differential Equation ◽

Arbitrary Dimension ◽

Derivative Operator ◽

Fractional Noise ◽

Fixed Point Principle ◽

Whole Space

We study a stochastic partial differential equation in the whole spacex∈ℝd, with arbitrary dimensiond≥1, driven by fractional noise and a pure jump Lévy space-time white noise. Our equation involves a fractional derivative operator. Under some suitable assumptions, we establish the existence and uniqueness of the global mild solution via fixed point principle.

On existence result of a class of nonlinear integral equation

Filomat ◽

10.2298/fil1711593b ◽

2017 ◽

Vol 31 (11) ◽

pp. 3593-3597

Author(s):

Ravindra Bisht

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Existence Result ◽

Nonlinear Integral Equation ◽

Continuous Functions ◽

Concave Functions ◽

Real Numbers ◽

Fixed Point Techniques ◽

Combining the approaches of functionals associated with h-concave functions and fixed point techniques, we study the existence and uniqueness of a solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) + ? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R) denotes the space of all continuous functions on [0,T] equipped with the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0, T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued functions in [0,T]xR.

Variational-hemivariational inverse problem for electro-elastic unilateral frictional contact problem

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip-2020-0051 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Othmane Baiz ◽

Hicham Benaissa ◽

Zakaria Faiz ◽

Driss El Moutawakil

Keyword(s):

Inverse Problem ◽

Inverse Problems ◽

Contact Problem ◽

Frictional Contact ◽

Hemivariational Inequalities ◽

Frictional Contact Problem ◽

AbstractIn the present paper, we study inverse problems for a class of nonlinear hemivariational inequalities. We prove the existence and uniqueness of a solution to inverse problems. Finally, we introduce an inverse problem for an electro-elastic frictional contact problem to illustrate our results.

Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

Advances in Difference Equations ◽

10.1186/s13662-020-02887-4 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Idris Ahmed ◽

Poom Kumam ◽

Jamilu Abubakar ◽

Piyachat Borisut ◽

Kanokwan Sitthithakerngkiet

Keyword(s):

Differential Equation ◽

Boundary Condition ◽

Fixed Point ◽

Fractional Differential Equation ◽

Periodic Boundary Condition ◽

Periodic Boundary ◽

Fixed Point Theorems ◽

Uniqueness Of The Solution ◽

Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

RANDOM DIFFERENTIAL EQUATIONS WITH RANDOM DELAYS

Stochastics and Dynamics ◽

10.1142/s0219493711003358 ◽

2011 ◽

Vol 11 (02n03) ◽

pp. 369-388 ◽

Cited By ~ 30

Author(s):

M. J. GARRIDO-ATIENZA ◽

A. OGROWSKY ◽

B. SCHMALFUSS

Keyword(s):

Dynamical System ◽

Differential Equation ◽

Existence Result ◽

Random Dynamical System ◽

Random Delay ◽

Random Differential Equation ◽

Autonomous Case ◽

Random Differential Equations ◽

We investigate a random differential equation with random delay. First the non-autonomous case is considered. We show the existence and uniqueness of a solution that generates a cocycle. In particular, the existence of an attractor is proved. Secondly we look at the random case. We pay special attention to the measurability. This allows us to prove that the solution to the random differential equation generates a random dynamical system. The existence result of the attractor can be carried over to the random case.

BSDE with rcll reflecting barrier driven by a Lévy process

Random Operators and Stochastic Equations ◽

10.1515/rose-2020-2029 ◽

2020 ◽

Vol 28 (1) ◽

pp. 63-77 ◽

Cited By ~ 1

Author(s):

Mohamed El Jamali ◽

Mohamed El Otmani

Keyword(s):

Differential Equation ◽

Stochastic Differential Equation ◽

Lévy Process ◽

Backward Stochastic Differential Equation ◽

American Option ◽

Levy Process ◽

Fair Price ◽

Penalization Method ◽

AbstractIn this paper, we study the solution of a backward stochastic differential equation driven by a Lévy process with one rcll reflecting barrier. We show the existence and uniqueness of a solution by means of the penalization method when the coefficient is stochastic Lipschitz. As an application, we give a fair price of an American option.

On the existence and uniqueness of a solution of a linear stochastic differential equation with respect to a logarithmic process

Ukrainian Mathematical Journal ◽

10.1007/bf02513440 ◽

1997 ◽

Vol 49 (6) ◽

pp. 966-975

Author(s):

A. Yu. Pilipenko

Keyword(s):

Differential Equation ◽

Stochastic Differential Equation ◽

Linear Stochastic Differential Equation ◽

Determination of a control parameter in a parabolic partial differential equation

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000006962 ◽

1991 ◽

Vol 33 (2) ◽

pp. 149-163 ◽

Cited By ~ 38

Author(s):

J. R. Cannon ◽

Yanping Lin ◽

Shingmin Wang

Keyword(s):

Differential Equation ◽

Partial Differential Equation ◽

Inverse Problem ◽

Global Solution ◽

Control Parameter ◽

Parabolic Partial Differential Equation ◽

Solution Pair ◽

Image Position

AbstractThe authors consider in this paper the inverse problem of finding a pair of functions (u, p) such thatwhere F, f, E, s, αi, βi, γi, gi, i = 1, 2, are given functions.The existence and uniqueness of a smooth global solution pair (u, p) which depends continuously upon the data are demonstrated under certain assumptions on the data.