Stochastic control with state constraints and non linear elliptic equations with infinite boundary conditions

2005 ◽  
pp. 75-91
Author(s):  
Jean-Michel Lasry ◽  
Pierre-Louis Lions
Keyword(s):  
Boundary Conditions ◽  
Stochastic Control ◽  
Elliptic Equations ◽  
State Constraints ◽  
Non Linear

Upper and lower solutions and semilinear second order elliptic equations with non-linear boundary conditions

1984 ◽  
Vol 97 ◽  
pp. 199-207 ◽  
Author(s):  
J. Mawhin ◽  
K. Schmitt
Keyword(s):  
Boundary Conditions ◽  
Elliptic Equations ◽  
General Framework ◽  
Upper And Lower Solutions ◽  
Second Order ◽  
Classical Solutions ◽  
Linear Boundary ◽  
Non Linear ◽  
Second Order Elliptic Equations

SynopsisA general framework is presented for the proof of the existence of classical solutions of second order elliptic equations which satisfy non-linear boundary conditions. The results obtained contain many of the known theorems for such problems and the approach used unifies the various methods of study based upon upper and lower solutions.

scholarly journals Non-linear boundary conditions for the convection-diffusion equation in lattice Boltzmann framework

2021 ◽  
pp. 116925
Author(s):  
Elham Kashani ◽  
Ali Mohebbi ◽  
Amir Ehsan Feili Monfared ◽  
Amir Raoof
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Lattice Boltzmann ◽  
Linear Boundary ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Non Linear

Non-local investigation of bifurcations of solutions of non-linear elliptic equations

2002 ◽  
Vol 66 (6) ◽  
pp. 1103-1130 ◽  
Author(s):  
Ya Sh Il'yasov
Keyword(s):  
Elliptic Equations ◽  
Non Linear ◽  
Non Local

Conduction of heat in a solid with periodic boundary conditions, with an application to the surface temperature of the moon

1953 ◽  
Vol 49 (2) ◽  
pp. 355-359 ◽  
Author(s):  
J. C. Jaeger
Keyword(s):  
Boundary Condition ◽  
Thermal Properties ◽  
Circular Cylinder ◽  
Boundary Conditions ◽  
Surface Temperature ◽  
Numerical Method ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
The Moon ◽  
Non Linear

The object of this note is to indicate a numerical method for finding periodic solutions of a number of important problems in conduction of heat in which the boundary conditions are periodic in the time and may be linear or non-linear. One example is that of a circular cylinder which is heated by friction along the generators through a rotating arc of its circumference, the remainder of the surface being kept at constant temperature; here the boundary conditions are linear but mixed. Another example, which will be discussed in detail below, is that of the variation of the surface temperature of the moon during a lunation; in this case the boundary condition is non-linear. In all cases the thermal properties of the solid will be assumed to be independent of temperature. Only the semi-infinite solid will be considered here, though the method applies equally well to other cases.

Approximations and boundary conditions for continuous-time threshold autoregressive processes

1994 ◽  
Vol 31 (4) ◽  
pp. 1103-1109 ◽  
Author(s):  
Rob J. Hyndman
Keyword(s):  
Time Series ◽  
Boundary Conditions ◽  
Continuous Time ◽  
Linear Time ◽  
Autoregressive Processes ◽  
Threshold Autoregressive ◽  
The Past ◽  
Time Threshold ◽  
Non Linear ◽  
The Way

Continuous-time threshold autoregressive (CTAR) processes have been developed in the past few years for modelling non-linear time series observed at irregular intervals. Several approximating processes are given here which are useful for simulation and inference. Each of the approximating processes implicitly defines conditions on the thresholds, thus providing greater understanding of the way in which boundary conditions arise.

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