scholarly journals The enclosure method for inverse obstacle scattering over a finite time interval: IV. Extraction from a single point on the graph of the response operator

2017 ◽  
Vol 25 (6) ◽  
Author(s):  
Masaru Ikehata
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Finite Time ◽  
Single Point ◽  
Obstacle Problems ◽  
Time Interval ◽  
Finite Time Interval ◽  
Partial Differential ◽  
Response Operator ◽  
Enclosure Method

AbstractA final and maybe the simplest formulation of the enclosure method applied to inverse obstacle problems governed by partial differential equations in a

scholarly journals The enclosure method for inverse obstacle scattering over a finite time interval: V. Using time-reversal invariance

2019 ◽  
Vol 27 (1) ◽  
pp. 133-149 ◽  
Author(s):  
Masaru Ikehata
Keyword(s):  
Wave Equation ◽  
Time Reversal ◽  
Finite Time ◽  
Single Point ◽  
Arbitrary Point ◽  
Time Interval ◽  
Finite Time Interval ◽  
Reversal Invariance ◽  
Enclosure Method ◽  
Space Wave

Abstract The wave equation is time-reversal invariant. The enclosure method, using a Neumann data generated by this invariance, is introduced. The method yields the minimum ball that is centered at a given arbitrary point and encloses an unknown obstacle embedded in a known bounded domain from a single point on the graph of the so-called response operator on the boundary of the domain over a finite time interval. The occurrence of the lacuna in the solution of the free space wave equation is positively used.

Identification of Forces in Vibrating Plates by Pointwise and Line Observations: Uniqueness and Stability

1995 ◽  
Author(s):  
Masahiro Yamamoto
Keyword(s):  
Finite Time ◽  
Large Time ◽  
Single Point ◽  
Time Interval ◽  
Finite Time Interval ◽  
Line Parallel ◽  
Vibrating Plates ◽  
External Forces ◽  
Spatially Varying

Abstract We consider determination of spatially varying external forces in a rectangle vibrating plate from displacement observed along a line parallel to a side of the plate over a finite time interval. For a suitable choice of the line and a sufficient large time interval, we prove the uniqueness of external forces and estimate them by appropriate norm of displacement. Moreover we discuss determination of external forces from displacement observed at a single point over a time interval.

A method for approximating the probability functions of a Markov chain

1988 ◽  
Vol 25 (4) ◽  
pp. 808-814 ◽  
Author(s):  
Keith N. Crank
Keyword(s):  
Markov Chain ◽  
Differential Equations ◽  
Finite Number ◽  
Continuous Time ◽  
Finite Time ◽  
The State ◽  
Time Interval ◽  
Continuous Time Markov Chain ◽  
Finite Time Interval ◽  
System Of Differential Equations

This paper presents a method of approximating the state probabilities for a continuous-time Markov chain. This is done by constructing a right-shift process and then solving the Kolmogorov system of differential equations recursively. By solving a finite number of the differential equations, it is possible to obtain the state probabilities to any degree of accuracy over any finite time interval.

scholarly journals Possibility of amoebas' aggregation in finite time

2013 ◽  
Vol 21 (1) ◽  
pp. 101-120
Author(s):  
Saïd Hilmi ◽  
Chérif Ziti
Keyword(s):  
Partial Differential Equations ◽  
Nonlinear System ◽  
Differential Equations ◽  
Finite Time ◽  
Blow Up ◽  
Dimensional Space ◽  
Partial Differential ◽  
Self Similar ◽  
Similar Solutions

Abstract The dynamic of amoebas in favorable circumstances is modeled by a nonlinear system of Partial Differential Equations arising in chemotaxis. The competition between different parameters of this system plays a major role in the process of aggregation. Throughout this paper, we prove the existence of self-similar solutions that blow up in finite time in a dimensional space and under specific circumstances depending upon the position of those parameters.

Bounded solutions for general time interval BSDEs with quadratic growth coefficients and stochastic conditions

2018 ◽  
Vol 18 (05) ◽  
pp. 1850034
Author(s):  
Huan-Huan Luo ◽  
Sheng-Jun Fan
Keyword(s):  
Differential Equations ◽  
Finite Time ◽  
Quadratic Growth ◽  
Time Interval ◽  
Finite Time Interval ◽  
Bounded Solutions ◽  
One Dimensional ◽  
Stochastic Conditions ◽  
New Ideas ◽  
General Time

This paper deals with bounded solutions for general time interval one-dimensional backward stochastic differential equations (BSDEs for short) with quadratic growth coefficients and stochastic conditions. Several general results of existence, uniqueness, stability and comparison for the bounded solutions are put forward and established, which improve considerably some existing works, even though for the case of finite time interval. Some new ideas are also developed to establish these results.

scholarly journals Parameter Estimation of Sigmoid Superpositions: Dynamical System Approach

2003 ◽  
Vol 15 (10) ◽  
pp. 2419-2455 ◽  
Author(s):  
Ivan Tyukin ◽  
Cees van Leeuwen ◽  
Danil Prokhorov
Keyword(s):  
Dynamical System ◽  
Parameter Estimation ◽  
Differential Equations ◽  
Linear Combination ◽  
Finite Time ◽  
System Approach ◽  
Effective Procedure ◽  
Time Interval ◽  
Sigmoid Function ◽  
Finite Time Interval

Superposition of sigmoid function over a finite time interval is shown to be equivalent to the linear combination of the solutions of a linearly parameterized system of logistic differential equations. Due to the linearity with respect to the parameters of the system, it is possible to design an effective procedure for parameter adjustment. Stability properties of this procedure are analyzed.

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