On the stability of recovering two sources and initial status in a stochastic hyperbolic-parabolic system

2021 ◽  
Author(s):  
Bin Wu ◽  
Jijun Liu
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Hyperbolic Equation ◽  
Wave Field ◽  
Time Derivative ◽  
Stability Index ◽  
Carleman Estimates ◽  
Conditional Stability ◽  
Coupling System ◽  
The Stability

Abstract Consider an inverse problem of determining two stochastic source functions and the initial status simultaneously in a stochastic thermoelastic system, which is constituted of two stochastic equations of different types, namely a parabolic equation and a hyperbolic equation. To establish the conditional stability for such a coupling system in terms of some suitable norms revealing the stochastic property of the governed system, we first establish two Carleman estimates with regular weight function and two large parameters for stochastic parabolic equation and stochastic hyperbolic equation, respectively. By means of these two Carleman estimates, we finally prove the conditional stability for our inverse problem, provided the source in the elastic equation be known near the boundary and the solution be in a prior bound set. Due to the lack of information about the time derivative of wave field at final moment, the stability index with respect to the wave field at final time is found to be halved, which reveals the special characteristic of our inverse problem for the coupling system.

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.

A non-iterative method for recovering the space-dependent source and the initial value simultaneously in a parabolic equation

2020 ◽  
Vol 28 (4) ◽  
pp. 499-516
Author(s):  
Zewen Wang ◽  
Shuli Chen ◽  
Shufang Qiu ◽  
Bin Wu
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Source Term ◽  
Dimensional Space ◽  
Conditional Stability ◽  
Finite Dimensional Space ◽  
Initial Value ◽  
Equation Problem ◽  
Inverse Solutions ◽  
Direct Problems

AbstractThis paper is concerned with the inverse problem for determining the space-dependent source and the initial value simultaneously in a parabolic equation from two over-specified measurements. By means of transforming information of the initial value into the source term and obtaining a combined source term, the parabolic equation problem is converted into a parabolic problem with homogeneous conditions. Then the considered inverse problem is formulated into a regularized minimization problem, which is implemented by the finite element method based on solving a sequence of well-posed direct problems. The uniqueness of inverse solutions are proved by the solvability of the corresponding variational problem, and the conditional stability as well as the convergence rate of regularized solutions are also provided. Then the error estimate of approximate regularization solutions is presented in the finite-dimensional space. The proposed method is a very fast non-iterative algorithm, and it can successfully solve the multi-dimensional inverse problem for recovering the space-dependent source and the initial value simultaneously. Numerical results of five examples including one- and two-dimensional cases show that the proposed method is efficient and robust with respect to data noise.

A FORECAST OF PRODUCTIVE LONGEVITY OF HOLSTEIN COWS BY INDIRECT SIGNS

2020 ◽  
Author(s):  
З.С. САНОВА
Keyword(s):  
Correlation Coefficient ◽  
Aging Process ◽  
Direct Relationship ◽  
Stability Index ◽  
Age At First Calving ◽  
Group I ◽  
Predicted Values ◽  
The Stability ◽  
Relationship Of ◽  
The Relationship

В статье представлены материалы о взаимосвязи продолжительности продуктивного использования коров с характеристикой устойчивости к деградации, с возрастом отела и удоем. В исследованной, разнородной по происхождению, группе животных для прогноза продуктивного периода коров, обусловленного устойчивостью к деградации и возрастом первого отела, пригодно уравнение регрессии, аргументами в котором являются индекс устойчивости, возраст первого отела в первой и второй степенях. Коэффициент корреляции межу предсказанными значениями продуктивного периода и его фактическими величинами в I группе составляет 0,502, во II - 0,604. При этом крайние варианты прогнозируются со статистическими ошибками 5 мес при оценке индекса устойчивости по 2 лактациям и 4,1 мес по 3, а средние варианты, соответственно, 1,6 и 1,51 мес. Индекс устойчивости к процессу старения является важной характеристикой биологических особенностей коров, определяющий их продуктивное долголетие. Его оценка по первым 2 и 3 лактациям имеет прямолинейную связь с продуктивным периодом (r=0,4109 и r=0,5270), соответственно. Зависимость продуктивного периода от возраста первого отела криволинейная — с увеличением возраста первого отела сокращается срок продуктивного использования, при возрасте первого отела более 1400 дней срок продуктивного использования колеблется от 1,33 до 1,41 лактации. Коэффициент корреляции между этими характеристиками коров составляет - 0,2164 в I и - 0,2620 во II группах. The article presents materials about the relationship of the duration of productive use of cows with the characteristic of resistance to degradation, with the age of calving and milk yield. In the studied group of animals, which is heterogeneous in origin, the regression equation is suitable for predicting the productive period of cows due to resistance to degradation and the age of the first calving, the arguments of which are the stability index, the age of the first calving in the first and second degrees. The correlation coefficient between the predicted values of the productive period and its actual values in group I is 0.502, in group II - 0.604. At the same time, the extreme variants are predicted with statistical errors of 5 months when evaluating the stability index for 2 lactations and 4.1 months for 3, and the average variants, respectively, are 1.6 and 1.51 months. The index of resistance to the aging process is an important characteristic of the biological characteristics of cows, which determines their productive longevity. Its estimate for the first 2 and 3 lactations has a direct relationship with the productive period (r=0.4109 and r=0.5270), respectively. The dependence of the productive period age at first calving curvilinear with increasing age at first calving reduces the time to productive use, while age at first calving of more than 1400 days, the period of productive use ranges from 1.33 to 1.41 lactation. The correlation coefficient between these characteristics of cows is-0.2164 in I and-0.2620 in II groups.

scholarly journals The BV solution of the parabolic equation with degeneracy on the boundary

2016 ◽  
Vol 14 (1) ◽  
pp. 272-282
Author(s):  
Huashui Zhan ◽  
Shuping Chen
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Well Posedness ◽  
Test Functions ◽  
The Stability

AbstractConsider a parabolic equation which is degenerate on the boundary. By the degeneracy, to assure the well-posedness of the solutions, only a partial boundary condition is generally necessary. When 1 ≤ α < p – 1, the existence of the local BV solution is proved. By choosing some kinds of test functions, the stability of the solutions based on a partial boundary condition is established.

An inverse problem for a parabolic equation with involution

2021 ◽  
Author(s):  
Batirkhan Turmetov ◽  
Bahtiyor Kadirkulov
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation

scholarly journals On a degenerate parabolic equation with Newtonian fluid∼non-Newtonian fluid mixed type

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sujun Weng
Keyword(s):  
Parabolic Equation ◽  
Newtonian Fluid ◽  
Weak Solutions ◽  
Mixed Type ◽  
Degenerate Parabolic Equation ◽  
Type Equation ◽  
Existence Of Weak Solutions ◽  
Degenerate Parabolic ◽  
The Stability ◽  
Increasing Function

AbstractWe study the existence of weak solutions to a Newtonian fluid∼non-Newtonian fluid mixed-type equation $$ {u_{t}}= \operatorname{div} \bigl(b(x,t){ \bigl\vert {\nabla A(u)} \bigr\vert ^{p(x) - 2}}\nabla A(u)+\alpha (x,t)\nabla A(u) \bigr)+f(u,x,t). $$ u t = div ( b ( x , t ) | ∇ A ( u ) | p ( x ) − 2 ∇ A ( u ) + α ( x , t ) ∇ A ( u ) ) + f ( u , x , t ) . We assume that $A'(s)=a(s)\geq 0$ A ′ ( s ) = a ( s ) ≥ 0 , $A(s)$ A ( s ) is a strictly increasing function, $A(0)=0$ A ( 0 ) = 0 , $b(x,t)\geq 0$ b ( x , t ) ≥ 0 , and $\alpha (x,t)\geq 0$ α ( x , t ) ≥ 0 . If $$ b(x,t)=\alpha (x,t)=0,\quad (x,t)\in \partial \Omega \times [0,T], $$ b ( x , t ) = α ( x , t ) = 0 , ( x , t ) ∈ ∂ Ω × [ 0 , T ] , then we prove the stability of weak solutions without the boundary value condition.

Studies on the Coordination Reaction of VO2+ and Tannic Acid in the Tannin Extract Desulfurization

2012 ◽  
Vol 239-240 ◽  
pp. 1573-1576
Author(s):  
Zhu Qing Gao ◽  
Xiao Dong Cai ◽  
Kai Cheng Ling
Keyword(s):  
Stability Constants ◽  
Tannic Acid ◽  
Ph Value ◽  
Protonation Constants ◽  
Conditional Stability ◽  
Tannin Extract ◽  
Acid Effect ◽  
Different Temperatures ◽  
The Stability ◽  
Apparent Stability

At different temperatures, the protonation constants of tannic acid and the complex apparent stability constants between tannic acid and VO2+ were determined by using pH potentimetric method. The results showed that the protonation constants and the complex apparent stability constants slightly decreased with the raising temperature. In accordance with the pH value in the tannin extract technology, the conditional stability constants of the complex were calculated on the basis of the acid effect of tannic acid and the hydrolysis effect of VO2+. It was found that pH greatly affected the stability constants of the complex , so pH must be strictly controlled in the tannin extract technology.

scholarly journals The stability index of a cactus

1977 ◽  
Vol 24 (2) ◽  
pp. 170-183
Author(s):  
Douglas D. Grant ◽  
D. A. Holton
Keyword(s):  
Connected Graph ◽  
Stability Index ◽  
The Stability

AbstractWe show that ifGis a connected graph of ordernsuch that no line lies in more than one cycle (in other words,Gis a cactus of ordern), then the stability index ofGis one of the integers 0, 1,n−7,n−6,n−5,n−4 orn.

Features of pubertal patients with schizophrenia neurocognitive profile

2017 ◽  
Vol 41 (S1) ◽  
pp. S430-S431
Author(s):  
Y. Barylnik ◽  
S. Pakhomova ◽  
D. Samoylova ◽  
J. Abrosimova ◽  
E. Kolesnichenko ◽  
...  
Keyword(s):  
Stability Index ◽  
Neurocognitive Disorders ◽  
Motor Speed ◽  
Structuring Element ◽  
Test Part ◽  
Psychic Disorders ◽  
Competing Interest ◽  
Neurocognitive Profile ◽  
The Stability ◽  
High Level

Identifying the patterns of neurocognitive disorders in pubertal schizophrenia is actual.MethodsBenton Test of visual retention, methods of forward and reverse bills, Bourdon correction sample, Wechsler's subtests (subtest 11 – “Encryption”, subtest 12 – “Labyrinths” 1, 2, 3, 4, 5), Trail Creating a Test Part A.ResultsAll patients were divided into 3 groups. The first group (schizophrenia) and second group (other psychic disorders) showed the worst results than healthy subjects. Qualitative analysis of the “Benton Test” results showed similar variations of difficulty and types of errors in the subjects of the first and second groups – ignoring the number of the figure sides, as well as difficulties in the structuring element of the image corners. The “Methods of forward and reverse bills” demonstrated the fatigue and attention instability. “Bourdon test” showed a high level of the stability index (K = 0.09). Wechsler's subtest “Encryption B” obtained poor results, indicating a pathological decrease in visual-motor speed. During the subtest “Labyrinths 1, 2, 3, 4, 5” the subjects of first and second groups exceeded the allowable time limit, but the first group of schizophrenia patients allowed more blunders during pubertal study (ignored the walls of the maze, torn pencil despite the given instructions). The test groups 1 and 2 while passing “Trail Creating a Test Part A” have shown good results – job data did not cause difficulties and carried out in accordance with the specified instructions.ConclusionsNeurocognitive disorders allow to confirm the presence of morphological and functional brain changes when endogenous mental illness occurs.Disclosure of interestThe authors have not supplied their declaration of competing interest.

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