Introduction Ill-Posedness of Inverse Problems for Differential and Integral Equations

2017 ◽  
pp. 1-19
Author(s):  
Alemdar Hasanov Hasanoğlu ◽  
Vladimir G. Romanov
Keyword(s):  
Inverse Problems ◽  
Integral Equations ◽  
Differential And Integral Equations

scholarly journals Qualitative Theory of Functional Differential and Integral Equations 2016

2017 ◽  
Vol 2017 ◽  
pp. 1-2
Author(s):  
Cemil Tunç ◽  
Bingwen Liu ◽  
Luís R. Sanchez ◽  
Mohsen Alimohammady ◽  
Octavian G. Mustafa ◽  
...  
Keyword(s):  
Integral Equations ◽  
Qualitative Theory ◽  
Functional Differential ◽  
Differential And Integral Equations

scholarly journals Dynamic near-field microwave diagnostics of lungs.

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
L.A. Bokeria ◽  
◽  
T.T. Kakuchaya ◽  
A.M. Kuular ◽  
Ye.S. Maksimovitch ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Inverse Problems ◽  
Integral Equations ◽  
Near Field ◽  
Experimental Studies ◽  
Heart Activity ◽  
Blood Content ◽  
Air Content ◽  
Microwave Diagnostics ◽  
Biomedical Diagnostics

Results of theoretical and experimental studies of the method of the near-field microwave tomography of the thorax are presented. Integral equations of inverse tomography problem of 3D blood- and air content inhomogeneities by data of multisensory measurements are obtained. Methods of air and blood content profiling in processes of breathing and heart activity by data of bistatic measurements of the scattered signal are proposed and solving algorithms of inverse problems are studied in the numerical simulation. Multifrequency and pulse measurements of scattered signals are carried out in processes of cardiorespiratory activity. By data of bistatic measurements of scattered signals parameters from the thorax, profiling relative air- and blood content profiles has been realized. Application possibilities of the method in the biomedical diagnostics are considered.

scholarly journals Convergence and Stability Results of Modified CUIA Iterative Scheme for Hyperbolic Convex Metric space

2021 ◽  
Vol 2089 (1) ◽  
pp. 012040
Author(s):  
Surjeet Singh Chauhan Gonder ◽  
Khushboo Basra
Keyword(s):  
Fixed Points ◽  
Integral Equations ◽  
Metric Space ◽  
Iterative Scheme ◽  
Real Life ◽  
Convex Metric Space ◽  
Convergence And Stability ◽  
Life Problems ◽  
Stability Results ◽  
Differential And Integral Equations

Abstract The iterative fixed points have numerous applications in locating the solution of some real-life problems which can be modelled into linear as well as nonlinear differential and integral equations. In this manuscript, first of all, a new iterative scheme namely Modified CUIA iterative scheme is introduced. We first prove a theorem to check the convergence of this iteration for Hyperbolic Convex metric space. The result is then supported with one example. Further, another theorem is proved establishing the weak T stability of modified CUIA iterative scheme on the above space.

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