scholarly journals Bi-quadratic polynomial approach for global convergent algorithm in high dimensions coefficient inverse problems

2011 ◽  
Vol 290 ◽  
pp. 012015
Author(s):  
Quan-Fang Wang
Keyword(s):  
Inverse Problems ◽  
Quadratic Polynomial ◽  
High Dimensions ◽  
Coefficient Inverse Problems ◽  
Convergent Algorithm

scholarly journals A triply cubic polynomials approach for globally convergent algorithm in coefficient inverse problems

2021 ◽  
Author(s):  
Quan-Fang Wang
Keyword(s):  
Inverse Problems ◽  
Nonlinear Term ◽  
Initial Boundary ◽  
Coefficient Function ◽  
Three Dimension ◽  
Boundary Problems ◽  
Globally Convergent ◽  
Coefficient Inverse Problems ◽  
Cubic Polynomials ◽  
Convergent Algorithm

In this paper, a triply cubic polynomials approach is proposed firstly for solving the globally convergent algorithm of coefficient inverse problems in three dimension. Using Taylor type expansion for three arguments to construct tripled cubic polynomials for the approximate solution as identifying coefficient function of parabolic initial-boundary problems, in which unknown coefficients appeared at nonlinear term. The presented computational approach is effective to execute in spatial 3D issues arising in real world. Further, the complete algorithm can be straightforwardly performed to lower or higher dimensions case

scholarly journals A triply cubic polynomials approach for globally convergent algorithm in coefficient inverse problems

2021 ◽  
Author(s):  
Quan-Fang Wang
Keyword(s):  
Inverse Problems ◽  
Nonlinear Term ◽  
Initial Boundary ◽  
Coefficient Function ◽  
Three Dimension ◽  
Boundary Problems ◽  
Globally Convergent ◽  
Coefficient Inverse Problems ◽  
Cubic Polynomials ◽  
Convergent Algorithm

In this paper, a triply cubic polynomials approach is proposed firstly for solving the globally convergent algorithm of coefficient inverse problems in three dimension. Using Taylor type expansion for three arguments to construct tripled cubic polynomials for the approximate solution as identifying coefficient function of parabolic initial-boundary problems, in which unknown coefficients appeared at nonlinear term. The presented computational approach is effective to execute in spatial 3D issues arising in real world. Further, the complete algorithm can be straightforwardly performed to lower or higher dimensions case

COEFFICIENT INVERSE PROBLEMS FOR THE PARABOLIC EQUATION WITH GENERAL WEAK DEGENERATION

2021 ◽  
Vol 9 (1) ◽  
pp. 91-106
Author(s):  
N. Huzyk ◽  
O. Brodyak
Keyword(s):  
Parabolic Equation ◽  
Inverse Problems ◽  
Existence And Uniqueness ◽  
Space Variable ◽  
Time Derivative ◽  
Classical Solutions ◽  
Linear Polynomial ◽  
Coefficient Inverse Problems ◽  
Degenerate Parabolic ◽  
Increasing Function

It is investigated the inverse problems for the degenerate parabolic equation. The mi- nor coeffcient of this equation is a linear polynomial with respect to space variable with two unknown time-dependent functions. The degeneration of the equation is caused by the monotone increasing function at the time derivative. It is established conditions of existence and uniqueness of the classical solutions to the named problems in the case of weak degeneration.

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