BOUNDARY CONDITIONS AND EXISTENCE RESULTS FOR LEVERMORE'S MOMENTS SYSTEM

2000 ◽  
Vol 10 (01) ◽  
pp. 127-152 ◽  
Author(s):  
P. LE TALLEC ◽  
J. P. PERLAT
Keyword(s):  
Boltzmann Equation ◽  
Boundary Conditions ◽  
Mathematical Analysis ◽  
Existence Results ◽  
Hyperbolic Structure ◽  
Dissipation Inequality ◽  
Moment Expansion ◽  
Linearized Problem ◽  
Flux Boundary Conditions ◽  
Weak Boundary Conditions

This paper considers the 14 moment expansion of the Boltzmann equation proposed by D. Levermore. After a brief review of this model, we derive weak boundary conditions compatible with the hyperbolic structure of the model, and express in average the microscopic boundary conditions imposed to the gas. This choice of half flux boundary conditions is justified by a mathematical analysis of the resulting linearized problem. Using standard parabolic regularization arguments and a specific dissipation inequality, we prove that the linearized problem has a unique solution.

Impulsive fractional differential inclusions with flux boundary conditions

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 953-961
Author(s):  
Hilmi Ergören
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Differential Inclusions ◽  
Existence Results ◽  
Fractional Differential Inclusions ◽  
Multivalued Maps ◽  
Flux Boundary Conditions ◽  
Fractional Differential

In this work we investigate some existence results for solutions of a boundary value problem for impulsive fractional differential inclusions supplemented with fractional flux boundary conditions by applying Bohnenblust-Karlin?s fixed point theorem for multivalued maps.

Ordinary Differential Equations with Nonlinear Boundary Conditions

2002 ◽  
Vol 9 (2) ◽  
pp. 287-294
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Lower And Upper Solutions ◽  
Iterative Technique ◽  
Monotone Iterative

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.

scholarly journals Nonlinear Differential Equations Modeling the Antarctic Circumpolar Current

2021 ◽  
Vol 23 (4) ◽  
Author(s):  
Jifeng Chu ◽  
Kateryna Marynets
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Topological Degree ◽  
Antarctic Circumpolar Current ◽  
Fixed Point Theorems ◽  
Nonlinear Differential Equations ◽  
Existence Results ◽  
Circumpolar Current ◽  
The Antarctic

AbstractThe aim of this paper is to study one class of nonlinear differential equations, which model the Antarctic circumpolar current. We prove the existence results for such equations related to the geophysical relevant boundary conditions. First, based on the weighted eigenvalues and the theory of topological degree, we study the semilinear case. Secondly, the existence results for the sublinear and superlinear cases are proved by fixed point theorems.

scholarly journals Existence Results for Fractional Differential Inclusions with Multivalued Term Depending on Lower-Order Derivative

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Xiaoyou Liu ◽  
Zhenhai Liu
Keyword(s):  
Boundary Conditions ◽  
Lower Order ◽  
Differential Inclusions ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Inclusion Problem ◽  
Fractional Differential Inclusions ◽  
Integral Boundary ◽  
Separated Boundary Conditions ◽  
Fractional Differential

This paper is concerned with a class of fractional differential inclusions whose multivalued term depends on lower-order fractional derivative with fractional (non)separated boundary conditions. The cases of convex-valued and non-convex-valued right-hand sides are considered. Some existence results are obtained by using standard fixed point theorems. A possible generalization for the inclusion problem with integral boundary conditions is also discussed. Examples are given to illustrate the results.

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