scholarly journals Well posedness for a singular two dimensional fractional initial boundary value problem with Bessel operator involving boundary integral conditions

2021 ◽  
Vol 6 (9) ◽  
pp. 9786-9812
Author(s):  
Said Mesloub ◽  
◽  
Faten Aldosari
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Boundary Integral ◽  
Bessel Operator ◽  
Well Posedness ◽  
Two Dimensional ◽  
Integral Conditions ◽  
Initial Boundary Value

scholarly journals Well-posedness of bounded solutions of the non-homogeneous initial-boundary value problem for the Ostrovsky–Hunter equation

2015 ◽  
Vol 12 (02) ◽  
pp. 221-248 ◽  
Author(s):  
Giuseppe Maria Coclite ◽  
Lorenzo di Ruvo
Keyword(s):  
Boundary Value Problem ◽  
Nonlinear Evolution ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Finite Depth ◽  
Well Posedness ◽  
Rotating Fluid ◽  
Bounded Solutions ◽  
Initial Boundary Value

The Ostrovsky–Hunter equation provides a model for small-amplitude long waves in a rotating fluid of finite depth. It is a nonlinear evolution equation. Here the well-posedness of bounded solutions for a non-homogeneous initial-boundary value problem associated with this equation is studied.

scholarly journals WELL-POSEDNESS FOR THE MASSIVE WAVE EQUATION ON ASYMPTOTICALLY ANTI-DE SITTER SPACETIMES

2012 ◽  
Vol 09 (02) ◽  
pp. 239-261 ◽  
Author(s):  
GUSTAV HOLZEGEL
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Energy Class ◽  
Well Posedness ◽  
De Sitter ◽  
Initial Boundary Value

In this paper, we prove a well-posedness theorem for the massive wave equation (with the mass satisfying the Breitenlohner–Freedman bound) on asymptotically anti-de Sitter spaces. The solution is constructed as a limit of solutions to an initial boundary value problem with boundary at a finite location in spacetime by finally pushing the boundary out to infinity. The solution obtained is unique within the energy class (but non-unique if the decay at infinity is weakened).

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