scholarly journals INVERSE PROBLEMS OF RECOVERING THE BOUNDARY DATA WITH INTEGRAL OVERDETERMINATION CONDITIONS

2018 ◽  
Vol 10 (2) ◽  
pp. 37-46
Author(s):  
S.G. Pyatkov ◽  
◽  
M.A. Verzhbitskii ◽  
Keyword(s):  
Inverse Problems ◽  
Boundary Data ◽  
Integral Overdetermination

Reconstruction of boundary data for a class of nonlinear inverse problems

2004 ◽  
Vol 12 (4) ◽  
pp. 369-385 ◽  
Author(s):  
M. Essaouini ◽  
A. Nachaoui ◽  
S. El Hajji
Keyword(s):  
Inverse Problems ◽  
Boundary Data ◽  
Nonlinear Inverse Problems

scholarly journals Inverse Problems with Unknown Boundary Conditions and Final Overdetermination for Time Fractional Diffusion-Wave Equations in Cylindrical Domains

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2541
Author(s):  
Jaan Janno
Keyword(s):  
Inverse Problems ◽  
Boundary Conditions ◽  
Boundary Data ◽  
Wave Equations ◽  
Fractional Diffusion ◽  
Unknown Boundary ◽  
Cylindrical Domain ◽  
Uniqueness Of Solutions ◽  
Final Time ◽  
Diffusion Wave

Inverse problems to reconstruct a solution of a time fractional diffusion-wave equation in a cylindrical domain are studied. The equation is complemented by initial and final conditions and partly given boundary conditions. Two cases are considered: (1) full boundary data on a lateral hypersurface of the cylinder are given, but the boundary data on bases of the cylinder are specified in a neighborhood of a final time; (2) boundary data on the whole boundary of the cylinder are specified in a neighborhood of the final time, but the cylinder is either a cube or a circular cylinder. Uniqueness of solutions of the inverse problems is proved. Uniqueness for similar problems in an interval and a disk is established, too.

scholarly journals Inverse Problems of Finding the Lowest Coefficient in the Elliptic Equation

2001 ◽  
Vol 14 (4) ◽  
pp. 528-542
Author(s):  
Alexander I. Kozhanov ◽  
Keyword(s):  
Elliptic Equation ◽  
Inverse Problems ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Additional Condition ◽  
Boundary Integral ◽  
Negative Coefficient ◽  
Integral Overdetermination Condition ◽  
Integral Overdetermination

The article is devoted to the study of problems of finding the non-negative coefficient q(t) in the elliptic equation utt + a2Δu − q(t)u = f(x, t) (x = (x1, . . . , xn) ∈ Ω ⊂ Rn, t ∈ (0, T), 0 < T < +∞, Δ — operator Laplace on x1, . . . , xn). These problems contain the usual boundary conditions and additional condition ( spatial integral overdetermination condition or boundary integral overdetermination condition). The theorems of existence and uniqueness are proved

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