scholarly journals On initial inverse problem for nonlinear couple heat with Kirchhoff type

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Danh Hua Quoc Nam
Keyword(s):  
Inverse Problem ◽  
Fixed Point ◽  
Main Tool ◽  
Cauchy Data ◽  
Final Model ◽  
Kirchhoff Type ◽  
Biological Phenomena ◽  
Banach’S Fixed Point Theorem ◽  
Unique Mild Solution ◽  
Well Posed

AbstractThe main objective of the paper is to study the final model for the Kirchhoff-type parabolic system. Such type problems have many applications in physical and biological phenomena. Under some smoothness of the final Cauchy data, we prove that the problem has a unique mild solution. The main tool is Banach’s fixed point theorem. We also consider the non-well-posed problem in the Hadamard sense. Finally, we apply truncation method to regularize our problem. The paper is motivated by the work of Tuan, Nam, and Nhat [Comput. Math. Appl. 77(1):15–33, 2019].

scholarly journals An inverse source problem for the stochastic wave equation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xiaoli Feng ◽  
Meixia Zhao ◽  
Peijun Li ◽  
Xu Wang
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Direct Problem ◽  
Inverse Source Problem ◽  
Time Data ◽  
Final Time ◽  
Stochastic Wave Equation ◽  
Unique Mild Solution ◽  
Well Posed ◽  
Class Of Functions

<p style='text-indent:20px;'>This paper is concerned with an inverse source problem for the stochastic wave equation driven by a fractional Brownian motion. Given the random source, the direct problem is to study the solution of the stochastic wave equation. The inverse problem is to determine the statistical properties of the source from the expectation and covariance of the final-time data. For the direct problem, it is shown to be well-posed with a unique mild solution. For the inverse problem, the uniqueness is proved for a certain class of functions and the instability is characterized. Numerical experiments are presented to illustrate the reconstructions by using a truncation-based regularization method.</p>

scholarly journals On The Initial Value Problem For Fractional Volterra Integrodifferential Equations With A Caputo - Fabrizio Derivative

2021 ◽  
Author(s):  
Nguyen Huy Tuan ◽  
Nguyen Anh Tuan ◽  
Donal O’regan ◽  
Vo Viet Tri
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Source Term ◽  
Main Tool ◽  
Integrodifferential Equations ◽  
Banach Fixed Point Theorem ◽  
Initial Value ◽  
Locally Lipschitz ◽  
Source Case ◽  
Well Posed

In this paper, time fractional integrodifferential equations with the Caputo - Fabrizio type derivative will be considered. In the case of a globally Lipschitz source term we obtain a global well - posed result on $\R^N$ for our problem. For the locally Lipschitz source case, we present existence and uniqueness and a finite time blow result for the solution. Our main tool is the Banach fixed point theorem and we extend  a  recent  paper of N.H. Tuan and Y. Zhou.

scholarly journals On the well posed solutions for nonlinear second order neutral difference equations

2016 ◽  
Vol 66 (4) ◽  
Author(s):  
Marek Galewski ◽  
Ewa Schmeidel
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equations ◽  
Existence Of Solutions ◽  
Main Tool ◽  
Second Order ◽  
Nonlinear Difference Equations ◽  
Neutral Difference Equations ◽  
Darbo Fixed Point Theorem ◽  
Well Posed

AbstractIn this work we investigate the existence of solutions, their uniqueness and finally dependence on parameters for solutions of second order neutral nonlinear difference equations. The main tool which we apply is Darbo fixed point theorem.

Inverse problem for one-dimensional wave equation with matrix potential

2019 ◽  
Vol 27 (2) ◽  
pp. 217-223 ◽  
Author(s):  
Ammar Khanfer ◽  
Alexander Bukhgeim
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Uniqueness Theorem ◽  
Cauchy Data ◽  
Global Uniqueness ◽  
One Dimensional ◽  
Matrix Potential ◽  
The Matrix ◽  
Real Matrices ◽  
Dimensional Wave

AbstractWe prove a global uniqueness theorem of reconstruction of a matrix-potential {a(x,t)} of one-dimensional wave equation {\square u+au=0}, {x>0,t>0}, {\square=\partial_{t}^{2}-\partial_{x}^{2}} with zero Cauchy data for {t=0} and given Cauchy data for {x=0}, {u(0,t)=0}, {u_{x}(0,t)=g(t)}. Here {u,a,f}, and g are {n\times n} smooth real matrices, {\det(f(0))\neq 0}, and the matrix {\partial_{t}a} is known.

Lipschitz stability for a semi-linear inverse stochastic transport problem

2020 ◽  
Vol 28 (2) ◽  
pp. 185-193
Author(s):  
Zhongqi Yin
Keyword(s):  
Inverse Problem ◽  
Main Tool ◽  
Terminal State ◽  
Lipschitz Stability ◽  
Unknown Parameters ◽  
Initial Displacement ◽  
Stochastic Transport ◽  
Random Term ◽  
Global Carleman Estimate ◽  
Stochastic Transport Equation

AbstractThis paper is addressed to a semi-linear stochastic transport equation with three unknown parameters. It is proved that the initial displacement, the terminal state and the random term in diffusion are uniquely determined by the state on partial boundary and a Lipschitz stability of the inverse problem is established. The main tool we employ is a global Carleman estimate for stochastic transport equations.

scholarly journals On New Type of F -Contractive Mapping for Quasipartial b -Metric Spaces and Some Results of Fixed-Point Theorem and Application

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
A. M. Zidan ◽  
Asma Al Rwaily
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Banach’S Fixed Point Theorem ◽  
Contractive Type ◽  
New Type

In this paper, we introduce the concept of new type of F -contractive type for quasipartial b-metric spaces and some definitions and lemmas. Also, we will prove a new fixed-point theorem in quasipartial b -metric spaces for F -contractive type mappings. In addition, we give an application which illustrates a situation when Banach’s fixed-point theorem for complete quasipartial b -metric spaces cannot be applied, while the conditions of our theorem are satisfying.

Exponential Stability Estimate of Fully Nonlinear Aceive Equation by Boundary Control

2011 ◽  
Vol 467-469 ◽  
pp. 1078-1083
Author(s):  
Dian Chen Lu ◽  
Ruo Yu Zhu
Keyword(s):  
Fixed Point ◽  
Exponential Stability ◽  
Dispersion Equation ◽  
Boundary Control ◽  
Existence And Uniqueness ◽  
Stability Estimate ◽  
Banach Fixed Point Theorem ◽  
Operator Semigroups ◽  
Fully Nonlinear ◽  
Well Posed

The well-posed problem for the fully nonlinear Aceive diffusion and dispersion equation on the domain [0, 1] is investigated by using boundary control. The existence and uniqueness of the solutions with the help of the Banach fixed point theorem and the theory of operator semigroups are verified. By using some inequalities and integration by parts, the exponential stability of the fully nonlinear Aceive diffusion and dispersion equation with the designed boundary feedback is also proved.

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