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Introduction to group analysis and invariant solutions of integro-differential equations
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2010 (engelsk)Inngår i: Lecture Notes in Physics, ISSN 0075-8450, Vol. 806, s. 57-111Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

In this chapter an introduction into applications of group analysis to equations with nonlocal operators, in particular, to integro-differential equations is given. The most known integro-differential equations are kinetic equations which form a mathematical basis in the kinetic theories of rarefied gases, plasma, radiation transfer, coagulation. Since these equations are directly associated with fundamental physical laws, there is special interest in studies of their solutions. The first section of this chapter contains a retrospective survey of different methods for constructing symmetries and finding invariant solutions of such equations. The presentation of the methods is carried out using simple model equations of small dimensionality, allowing the reader to follow the calculations in detail. In the next section, the classical scheme of the construction of determining equations of an admitted Lie group is generalized for equations with nonlocal operators. In the concluding sections of this chapter, the developed regular method of obtaining admitted Lie groups is illustrated by applications to some known integro-differential equations.

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Springer , 2010. Vol. 806, s. 57-111
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Identifikatorer
URN: urn:nbn:se:bth-7604DOI: 10.1007/978-90-481-3797-8_2Lokal ID: oai:bth.se:forskinfo0661B821FCB069E0C1257811004942B7OAI: oai:DiVA.org:bth-7604DiVA, id: diva2:835247
Tilgjengelig fra: 2012-09-18 Laget: 2011-01-07 Sist oppdatert: 2015-06-30bibliografisk kontrollert

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