Well-posedness of boundary-value problems for equation (1) in the case of commuting self-adjoint A and B

1997 ◽  
pp. 17-33
Author(s):  
Alexander Ya. Shklyar
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Well Posedness

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.

scholarly journals Boundary-value problems in a layer for evolutionary pseudo-differential equations with integral conditions

2018 ◽  
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Integral Condition ◽  
Well Posedness ◽  
Integral Conditions ◽  
Pseudo Differential Equation ◽  
Necessary And Sufficient ◽  
Well Posed

Boundary-value problems for evolutionary pseudo-differential equations with an integral condition are studied. Necessary and sufficient conditions of well-posedness are obtained for these problems in the Schwartz spaces. Existence of a well-posed boundary-value problem is proved for each evolutionary pseudo-differential equation.

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