An inverse source problem for pseudo-parabolic equation with Caputo derivative

2021 ◽  
Author(s):  
Le Dinh Long ◽  
Nguyen Hoang Luc ◽  
Salih Tatar ◽  
Dumitru Baleanu ◽  
Nguyen Huu Can
Keyword(s):  
Parabolic Equation ◽  
Caputo Derivative ◽  
Inverse Source Problem

scholarly journals An inverse source problem for a two dimensional time fractional diffusion equation with involution

2021 ◽  
Author(s):  
Batirkhan Turmetov ◽  
B. J. Kadirkulov
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Diffusion Equation ◽  
Fourier Method ◽  
Dirichlet Condition ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Inverse Source Problem ◽  
Two Dimensional ◽  
Time Fractional Diffusion Equation

In this paper, we consider a two-dimensional generalization of the parabolic equation. Using the Fourier method, we study the solvability of the inverse problem with the Dirichlet condition and periodic conditions.

scholarly journals Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Oleg Y. Imanuvilov ◽  
Yavar Kian ◽  
Masahiro Yamamoto
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Boundary Data ◽  
Stability Estimate ◽  
Carleman Estimate ◽  
Parabolic Problems ◽  
Conditional Stability ◽  
Inverse Source Problem ◽  
Lateral Boundary ◽  
Spatial Component

Abstract For a parabolic equation in the spatial variable x = ( x 1 , … , x n ) {x=(x_{1},\ldots,x_{n})} and time t, we consider an inverse problem of determining a coefficient which is independent of one spatial component x n {x_{n}} by lateral boundary data. We apply a Carleman estimate to prove a conditional stability estimate for the inverse problem. Also, we prove similar results for the corresponding inverse source problem.

scholarly journals Numerical simulation for an inverse source problem in a degenerate parabolic equation

2015 ◽  
Vol 39 (23-24) ◽  
pp. 7537-7553 ◽  
Author(s):  
Xiao-Bo Rao ◽  
Yu-Xin Wang ◽  
Kun Qian ◽  
Zui-Cha Deng ◽  
Liu Yang
Keyword(s):  
Numerical Simulation ◽  
Parabolic Equation ◽  
Degenerate Parabolic Equation ◽  
Inverse Source Problem ◽  
Degenerate Parabolic

Inverse source problem for parabolic equation with the condition of integral observation in time

2018 ◽  
Vol 26 (4) ◽  
pp. 523-539 ◽  
Author(s):  
Aleksey I. Prilepko ◽  
Vitaly L. Kamynin ◽  
Andrew B. Kostin
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Inverse Problems ◽  
Unique Solvability ◽  
Existence And Uniqueness ◽  
Additional Condition ◽  
Sufficient Conditions ◽  
Inverse Source Problem ◽  
Source Determination ◽  
Integral Observation

Abstract We consider the inverse problem of source determination in nonuniformly parabolic equation under the additional condition of integral observation. We investigate the questions of existence and uniqueness of solution. Two types of sufficient conditions for the unique solvability of the inverse problem are obtained. Examples of inverse problems are given for which the conditions of the proved theorems are fulfilled.

scholarly journals Existence and regularity results for stochastic fractional pseudo-parabolic equations driven by white noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Tran Ngoc Thach ◽  
Devendra Kumar ◽  
Nguyen Hoang Luc ◽  
Nguyen Huy Tuan
Keyword(s):  
Parabolic Equation ◽  
White Noise ◽  
Linear Space ◽  
Parabolic Equations ◽  
Caputo Derivative ◽  
Direct Problem ◽  
Mild Solutions ◽  
Fractional Caputo Derivative ◽  
Existence And Regularity Results ◽  
Regularity Results

<p style='text-indent:20px;'>Solutions of a direct problem for a stochastic pseudo-parabolic equation with fractional Caputo derivative are investigated, in which the non-linear space-time-noise is assumed to satisfy distinct Lipshitz conditions including globally and locally assumptions. The main aim of this work is to establish some existence, uniqueness, regularity, and continuity results for mild solutions.</p>

Numerical Study of Inverse Source Problem for Internal Degenerate Parabolic Equation

2020 ◽  
Vol 18 (01) ◽  
pp. 2050032
Author(s):  
M. Alahyane ◽  
I. Boutaayamou ◽  
A. Chrifi ◽  
Y. Echarroudi ◽  
Y. Ouakrim
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Parabolic Equation ◽  
Degenerate Parabolic Equation ◽  
Augmented Lagrangian ◽  
Numerical Study ◽  
Augmented Lagrangian Method ◽  
Inverse Source Problem ◽  
Discrete Solution ◽  
Degenerate Parabolic

This paper is devoted to numerical analysis of an inverse source problem in a degenerate parabolic equation. The aims of this work are to show the well-posedness of the discrete inverse problem and its convergence to the continuous one. For this, we reformulate first the encountered inverse problem to a regularized optimal control one. Then, we approximate our optimal control problem by finite element method and we show the existence of the discrete solution and its convergence to the continuous one. Finally, in order to confirm the efficiency of the proposed scheme, some numerical results are obtained using the augmented Lagrangian method.

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