On the global stability of large solutions for the Boussinesq equations with Navier boundary conditions

2021 ◽  
Author(s):  
Weinan Wang
Keyword(s):  
Boundary Conditions ◽  
Global Stability ◽  
Boussinesq Equations ◽  
Navier Boundary Conditions ◽  
Large Solutions

scholarly journals On a p x -Biharmonic Kirchhoff Problem with Navier Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Hafid Lebrimchi ◽  
Mohamed Talbi ◽  
Mohammed Massar ◽  
Najib Tsouli
Keyword(s):  
Boundary Conditions ◽  
Variational Methods ◽  
Nontrivial Solution ◽  
Existence Of Solutions ◽  
Type Problem ◽  
Navier Boundary Conditions ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem ◽  
Kirchhoff Problem

In this article, we study the existence of solutions for nonlocal p x -biharmonic Kirchhoff-type problem with Navier boundary conditions. By different variational methods, we determine intervals of parameters for which this problem admits at least one nontrivial solution.

ON A CLASS OF FOURTH ORDER NONLINEAR ELLIPTIC EQUATIONS UNDER NAVIER BOUNDARY CONDITIONS

2010 ◽  
Vol 08 (02) ◽  
pp. 185-197 ◽  
Author(s):  
F. J. S. A. CORRÊA ◽  
J. V. GONCALVES ◽  
ANGELO RONCALLI
Keyword(s):  
Boundary Conditions ◽  
Fixed Points ◽  
Fourth Order ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Compact Operators ◽  
Schmidt Method ◽  
Navier Boundary Conditions ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity

We employ arguments involving continua of fixed points of suitable nonlinear compact operators and the Lyapunov–Schmidt method to prove existence and multiplicity of solutions in a class of fourth order non-homogeneous resonant elliptic problems. Our main result extends even similar ones known for the Laplacian.

Optimal boundary control for the stationary Boussinesq equations with variable density

2019 ◽  
Vol 22 (05) ◽  
pp. 1950031
Author(s):  
José Luiz Boldrini ◽  
Exequiel Mallea-Zepeda ◽  
Marko Antonio Rojas-Medar
Keyword(s):  
Boundary Conditions ◽  
Optimality Conditions ◽  
Boundary Control ◽  
Boussinesq Equations ◽  
Variable Density ◽  
Control Problems ◽  
Dynamical Equations ◽  
Optimal Boundary ◽  
Optimal Boundary Control ◽  
Boundary Control Problems

Certain classes of optimal boundary control problems for the Boussinesq equations with variable density are studied. Controls for the velocity vector and temperature are applied on parts of the boundary of the domain, while Dirichlet and Navier friction boundary conditions for the velocity and Dirichlet and Robin boundary conditions for the temperature are assumed on the remaining parts of the boundary. As a first step, we prove a result on the existence of weak solution of the dynamical equations; this is done by first expressing the fluid density in terms of the stream-function. Then, the boundary optimal control problems are analyzed, and the existence of optimal solutions are proved; their corresponding characterization in terms of the first-order optimality conditions are obtained. Such optimality conditions are rigorously derived by using a penalty argument since the weak solutions are not necessarily unique neither isolated, and so standard methods cannot be applied.

Sign in / Sign up

Export Citation Format

Share Document