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.

On Solvability and Well-Posedness of Boundary Value Problems for Nonlinear Hyperbolic Equations of the Fourth Order

2008 ◽  
Vol 15 (3) ◽  
pp. 555-569
Author(s):  
Tariel Kiguradze
Keyword(s):  
Hyperbolic Equation ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Hyperbolic Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Nonlinear Hyperbolic Equation ◽  
Well Posedness ◽  
Nonlinear Hyperbolic Equations ◽  
Right Hand

Abstract In the rectangle Ω = [0, a] × [0, b] the nonlinear hyperbolic equation 𝑢(2,2) = 𝑓(𝑥, 𝑦, 𝑢) with the continuous right-hand side 𝑓 : Ω × ℝ → ℝ is considered. Unimprovable in a sense sufficient conditions of solvability of Dirichlet, Dirichlet–Nicoletti and Nicoletti boundary value problems are established.

Partial Higher-Order Specifications1

1992 ◽  
Vol 16 (2) ◽  
pp. 101-126
Author(s):  
Egidio Astesiano ◽  
Maura Cerioli
Keyword(s):  
Sufficient Conditions ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Important Case ◽  
Deduction System ◽  
Closure Properties ◽  
Inference System ◽  
Conditional Specification ◽  
Necessary And Sufficient

In this paper the classes of extensional models of higher-order partial conditional specifications are studied, with the emphasis on the closure properties of these classes. Further it is shown that any equationally complete inference system for partial conditional specifications may be extended to an inference system for partial higher-order conditional specifications, which is equationally complete w.r.t. the class of all extensional models. Then, applying some previous results, a deduction system is proposed, equationally complete for the class of extensional models of a partial conditional specification. Finally, turning the attention to the special important case of termextensional models, it is first shown a sound and equationally complete inference system and then necessary and sufficient conditions are given for the existence of free models, which are also free in the class of term-generated extensional models.

The weighted Cauchy problem for linear functional differential equations with strong singularities

2011 ◽  
Vol 18 (3) ◽  
pp. 577-586
Author(s):  
Zaza Sokhadze
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Initial Point ◽  
Higher Order ◽  
Well Posedness ◽  
Deviating Arguments ◽  
Functional Differential

Abstract The sufficient conditions of well-posedness of the weighted Cauchy problem for higher order linear functional differential equations with deviating arguments, whose coefficients have nonintegrable singularities at the initial point, are found.

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