Boundary-value problems for a nonlinear hyperbolic equation with divergent part and Lévy Laplacian

2012 ◽  
Vol 64 (2) ◽  
pp. 273-281 ◽  
Author(s):  
M. N. Feller
Keyword(s):  
Hyperbolic Equation ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Nonlinear Hyperbolic Equation ◽  
Divergent Part ◽  
Lévy Laplacian

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.

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