On the Dirichlet problem in a characteristic rectangle for higher order linear hyperbolic equations

2002 ◽  
Vol 50 (8) ◽  
pp. 1153-1178 ◽  
Author(s):  
T. Kiguradze ◽  
V. Lakshmikantham
Keyword(s):  
Dirichlet Problem ◽  
Hyperbolic Equations ◽  
Higher Order ◽  
Order Linear ◽  
Linear Hyperbolic Equations

On the Correctness of the Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Hyperbolic Equations

1999 ◽  
Vol 6 (5) ◽  
pp. 447-470
Author(s):  
T. Kiguradze
Keyword(s):  
Dirichlet Problem ◽  
Hyperbolic Equation ◽  
Fourth Order ◽  
Trivial Solution ◽  
Hyperbolic Equations ◽  
Homogeneous Problem ◽  
Linear Hyperbolic Equation ◽  
Order Linear ◽  
Linear Hyperbolic Equations

Abstract It is proved that the Dirichlet problem is correct in the characteristic rectangle 𝐷𝑎𝑏 = [0, 𝑎] × [0, 𝑏] for the linear hyperbolic equation with the summable in 𝐷𝑎𝑏 coefficients 𝑝0, 𝑝1, 𝑝2, 𝑝3 and 𝑞 if and only if the corresponding homogeneous problem has only the trivial solution. The effective and optimal in some sense restrictions on 𝑝0, 𝑝1, 𝑝2 and 𝑝3 guaranteeing the correctness of the Dirichlet problem are established.

Multi-dimensional periodic problems for higher-order linear hyperbolic equations

2019 ◽  
Vol 26 (2) ◽  
pp. 235-256
Author(s):  
Tariel Kiguradze ◽  
Noha Al Jaber
Keyword(s):  
Hyperbolic Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Dimensional Case ◽  
Well Posedness ◽  
Two Dimensional ◽  
Order Linear ◽  
Periodic Problems ◽  
Necessary And Sufficient ◽  
Linear Hyperbolic Equations

Abstract For higher-order linear hyperbolic equations the problem on periodic solutions is investigated. The concepts of associated problems, and α-well-posedness are introduced. Necessary and sufficient conditions of well-posedness in the two-dimensional case, as well as unimprovable sufficient conditions of well-posedness and α-well-posedness in the multi-dimensional case are established.

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