Qualitative difference between solutions for a model of the Boltzmann equation in the linear and nonlinear cases

Khachatryan, A. Kh.; Khachatryan, Kh. A.

doi:10.1007/s11232-012-0116-4

Theor Math Phys

2012

DOI: 10.1007/s11232-012-0116-4

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Qualitative difference between solutions for a model of the Boltzmann equation in the linear and nonlinear cases

A. Kh. Khachatryan

Kh. A. Khachatryan

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Cited by 15 publications

(1 citation statement)

References 6 publications

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“…The system (1) arises in discrete problems of radiative transfer theory (see [1,2]). Such type of system also arises in kinetic theory of gases and p-adic string theory (see [3][4][5]).…”

mentioning

confidence: 99%

On Solvability of an Infinite Nonlinear System of Algebraic Equations With Teoplitz–hankel Matrices

Khachatryan¹,

Avetisyan²

2017

Proc. YSU A: Phys. Math. Sci.

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“…The system (1) arises in discrete problems of radiative transfer theory (see [1,2]). Such type of system also arises in kinetic theory of gases and p-adic string theory (see [3][4][5]).…”

mentioning

confidence: 99%

On Solvability of an Infinite Nonlinear System of Algebraic Equations With Teoplitz–hankel Matrices

Khachatryan¹,

Avetisyan²

2017

Proc. YSU A: Phys. Math. Sci.

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Qualitative difference between solutions of stationary model Boltzmann equations in the linear and nonlinear cases

Khachatryan

2014

Theor Math Phys

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Positive solubility of some classes of non-linear integral equations of Hammerstein type on the semi-axis and on the whole line

Khachatryan¹

2015

Izv. Math.

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We study certain classes of non-linear Hammerstein integral equations on the semi-axis and the whole line. These classes of equations arise in the theory of radiative transfer in nuclear reactors, in the kinetic theory of gases, and for travelling waves in non-linear Richer competition systems. By combining special iteration methods with the methods of construction of invariant cone segments for the appropriate nonlinear operator, we are able to prove constructive existence theorems for positive solutions in various function spaces. We give illustrative examples of equations satisfying all the hypotheses of our theorems.

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Qualitative difference between solutions for a model of the Boltzmann equation in the linear and nonlinear cases

Cited by 15 publications

References 6 publications

On Solvability of an Infinite Nonlinear System of Algebraic Equations With Teoplitz–hankel Matrices

On Solvability of an Infinite Nonlinear System of Algebraic Equations With Teoplitz–hankel Matrices

Qualitative difference between solutions of stationary model Boltzmann equations in the linear and nonlinear cases

Positive solubility of some classes of non-linear integral equations of Hammerstein type on the semi-axis and on the whole line

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