A nonlocal inverse problem for a mixed-type equation

2011 ◽  
Vol 55 (2) ◽  
pp. 61-74 ◽  
Author(s):  
K. B. Sabitov ◽  
N. V. Martem’yanova
Keyword(s):  
Inverse Problem ◽  
Mixed Type ◽  
Type Equation ◽  
Mixed Type Equation

THE BOUNDARY VALUE PROBLEM OF FINDING A RIGHT-HAND SIDE FOR MIXED TYPE EQUATION WITH CHAPLYGIN’S TYPE OPERATOR

2021 ◽  
Vol 9 (4) ◽  
pp. 26-50
Author(s):  
K.B. Sabitov ◽  
◽  
I.A. Burkhanova (Haji) ◽  
Keyword(s):  
Inverse Problem ◽  
Mixed Type ◽  
Orthogonal Series ◽  
Type Equation ◽  
Transition Line ◽  
Mixed Type Equation ◽  
Uniqueness Criterion ◽  
Right Hand ◽  
Definition Of ◽  
The Given

In this paper, we study the inverse problem for a mixed-type equation with power degeneracy on a transition line by definition of its right-hand side, depending on the spatial coordinate. The theory of identity has been proved. In the case of degree degeneracy, the uniqueness criterion for the solution of the problem is proved, and the solution itself is con- structed in the form of a sum of orthogonal series. The consistency of series in the class of solutions of the given equation is justified and the validity of the solution with respect to the boundary conditions is proved.

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