АСИМПТОТИКА ВИРІШЕННЯ ТРАНСПОРТНОГО ЕВОЛЮЦІЙНОГО РІВНЯННЯ

Автор(и)

  • Yevgeny Vasilevich Cheremnikh Lviv Polytechnic National University, Lviv, Ukraine
  • Fatima Diaba Badji Mokhtar-Annaba, Algeria, Algeria
  • Galina Vladimirovna Ivasyk Lviv Polytechnic National University, Lviv, Ukraine

DOI:

https://doi.org/10.32626/2308-5878.2010-4.208-223

Ключові слова:

spectrum, transport operator, Friedrichs' model, semigroup.

Анотація

Authors consider in the space the transport operator. To obtain the representation of the solution of the equation authors introduce some integral (like known expression the semigroup by the resolvent) and prove directly that this integral is corresponding semigroup. To simplify the calculus the authors reduce the operator L to some Friedrichs' model using Fourier transformation.

Посилання

Lehner I. The spectrum of neutron transport operator for the infinit slab, I.Math. Mech / I. Lehner. — 1962. — №. 2. — P. 173—181.

Kuperin Yu. A. Spectral analysis of a one speed transmission operator and functional model. Funct. anal. and its appl / Yu. A. Kuperin, S. N. Naboko, R. V. Romanov. — 1999. — Vol. 33, №. 2. — P. 47—58.

Diaba F. On the point spectrum of transport operator. Math. Func. Anal. and Topology / F. Diaba, E. V. Cheremnikh. — 2005. — Vol. 11, №. 1. — P. 21—36.

Ivasyk G. V. Friedrich's model for transport operator / G. V. Ivasyk, E. V. Cheremnikh // Journal of National University «Lvivska Politechnika», Phys. and math. sciencesю. — 2009. — Vol. 643, №. 643. — P. 30—36.

Cheremnikh E. V. Sufficient condition of finiteness of point spectrum (in print) / E. V. Cheremnikh, G. V. Ivasyk.

Gohberg I. Z. Introduction to the theory of linear non self-adjoint operators / I. Z. Gohberg, M. G. Krein. — 1965. — 448 p.

Bremermann H. Distributions, Complex Variables and Fourier Transforms / H. Bremermann, 1965.

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Опубліковано

2010-10-16

Номер

2010: Математичне та комп'ютерне моделювання. Серія: Фізико-математичні науки. Випуск 4

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