ON A BOUNDARY VALUE PROBLEM FOR THE PLANE BROADWELL MODEL: EXACT SOLUTIONS AND NUMERICAL SIMULATION

1995 ◽  
Vol 05 (03) ◽  
pp. 253-266 ◽  
Author(s):  
A.V. BOBYLEV ◽  
E. GABETTA ◽  
L. PARESCHI
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Behavior ◽  
Boundary Value Problem ◽  
Exact Solutions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Stationary Solutions ◽  
Model Equations ◽  
Initial Boundary Value

The initial boundary value problem for the Broadwell model equations in a half infinite channel with an infinitely small hole is considered. It is proved that this boundary value problem has no unique solution for sufficiently large concentration of the gas. There are at least two different solutions, we have constructed them in explicit form. The existence of stationary solutions for the corresponding initial boundary value problem is then numerically investigated. The results indicate a unique asymptotic behavior of the model, very close to one of the two predicted stationary solutions.

scholarly journals The first initial-boundary value problem of parabolic Monge–Ampère equations outside a bowl-shaped domain

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Limei Dai ◽  
Huihui Cheng
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Boundary Value ◽  
Weaker Conditions ◽  
Monge Ampere ◽  
Shaped Domain

AbstractIn this paper, we study the parabolic Monge–Ampère equations $-u_{t}\det (D^{2}u)=g$ − u t det ( D 2 u ) = g outside a bowl-shaped domain with g being the perturbation of $g_{0}(|x|)$ g 0 ( | x | ) at infinity. Under the weaker conditions compared with the problem outside a cylinder, we obtain the existence and uniqueness of viscosity solutions with asymptotic behavior for the first initial-boundary value problem by using the Perron method.

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