On a Linear Inverse Problem for a Multidimensional Mixed-Type Equation

被引:0
作者
S. Z. Dzhamalov
R. R. Ashurov
机构
[1] Uzbekistan Academy of Sciences,Romanovskiy Institute of Mathematics
来源
Differential Equations | 2019年 / 55卷
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摘要
We study the well-posedness of a linear inverse problem for a multidimensional mixed-type equation including the classical equations of elliptic, hyperbolic, and parabolic types as special cases. For this problem, using the “ε-regularization,” a priori estimate, and successive approximationmethods, we prove the existence and uniqueness theorems for the solution in some function class.
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页码:34 / 45
页数:11
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共 14 条
[1]  
Kozhanov A.I.(2004)Nonlinear loaded equations and inverse problems Comput. Math. Math. Phys. 44 658-678
[2]  
Sabitov K.B.(2011)A nonlocal inverse problem for a mixed-type equation Russ. Math. 55 61-74
[3]  
Martem’yanova N.V.(2015)Inverse problem for degenerate parabolic-hyperbolic equation with nonlocal boundary condition Russ. Math. 59 39-50
[4]  
Sabitov K.B.(2017)The inverse problem for the Lavrent’ev–Bitsadze equation connected with the search of elements in the right-hand side Russ. Math. 61 36-48
[5]  
Sidorov S.N.(2016)Linear inverse problem for second-order mixed-type equation of the second kind with nonlocal boundary conditions in the three-dimensional case The linear inverse problem for the Tricomi equation in three-dimensional space, Vestn. KRAUNTs 2 12-17
[6]  
Sabitov K.B.(2017)Loaded equations and their applications Vestn. KRAUNTs 1 7-13
[7]  
Martem’yanova N.V.(1983)On the correctness of a nonlocal problem for the second order mixed type equations of the second kind in a rectangle Differ. Equations 19 74-81
[8]  
Dzhamalov S.Z.(2016)Nonlocal boundary-value problems for some equations of mixed type in the rectangle IIUM J. 17 95-104
[9]  
Dzhamalov S.Z.(1985)A nonlocal boundary-value problem for an equation of mixed type Sib. Mat. Zh. 26 162-164
[10]  
Nakhushev A.M.(1991)On a nonlocal boundary value problem for a second-order mixed type equation of the second kind Differ. Equations 27 54-63