Conditional Correctness of the Internal Boundary Value Problem of the Pseudoparabolic Equation with a Changing Time Direction

2020 ◽  
Vol 32 (1) ◽  
pp. 49-60
Author(s):  
Kudratillo Sadridinovich Fayazov ◽  
Zamira Shamshaddinovna Abdullayeva
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Internal Boundary ◽  
Pseudoparabolic Equation ◽  
Time Direction

Sand erosion as an internal boundary value problem

2014 ◽  
Vol 10 (3) ◽  
pp. 333-342 ◽  
Author(s):  
Hans Muhlhaus ◽  
Lutz Gross ◽  
Alexander Scheuermann
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Internal Boundary ◽  
Sand Erosion

THE METHOD OF FUNDAMENTAL SOLUTIONS FOR AN INVERSE INTERNAL BOUNDARY VALUE PROBLEM FOR THE BIHARMONIC EQUATION

2009 ◽  
Vol 06 (04) ◽  
pp. 557-567 ◽  
Author(s):  
D. LESNIC ◽  
A. ZEB
Keyword(s):  
Boundary Value Problem ◽  
Biharmonic Equation ◽  
Numerical Solutions ◽  
Least Squares Method ◽  
Regularization Parameter ◽  
Boundary Value ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Internal Boundary ◽  
Unknown Boundary

In this paper, an inverse internal boundary value problem associated to the biharmonic equation is considered. The problem consists of determining unknown boundary conditions from extra interior measurements. The method of fundamental solutions (MFS) is used to discretize the problem and the resulting ill-conditioned system of linear equations is solved using the Tikhonov regularization technique. It is shown that, unlike the least-squares method, the MFS-regularization numerical technique produces stable and accurate numerical solutions for an appropriate choice of the regularization parameter given by the L-curve criterion.

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