scholarly journals Stability analysis and error estimate of flowfield-dependent variation (FDV) method for first order linear hyperbolic equations

2015 ◽  
Vol 285 ◽  
pp. 125-131
Author(s):  
Moongyu Park
Keyword(s):  
Stability Analysis ◽  
Error Estimate ◽  
Hyperbolic Equations ◽  
Order Linear ◽  
First Order ◽  
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.

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