Geodesic
On one Sobolev type mathematical model in quasi-Banach spaces
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 1, pp. 137-142 Cet article a éte moissonné depuis la source Math-Net.Ru

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The theory of Sobolev type equations experiences an epoch of blossoming. In this article the theory of higher order Sobolev type equations with relatively spectrally bounded operator pencils, previously developed in Banach spaces, is transferred to quasi-Banach spaces. We use already well proved for solving Sobolev type equations phase space method, consisting in reduction of singular equation to regular one defined on some subspace of initial space. The propagators and the phase space of complete higher order Sobolev type equations are constructed. Abstract results are illustrated by specific examples. The Boussinesq–Love equation in quasi-Banach space is considered as application.
Keywords: Sobolev type equations; quasi-Banach spaces; propagators; phase space. 
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A. A. Zamyshlyaeva; H. M. Al Helli. On one Sobolev type mathematical model in quasi-Banach spaces. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 1, pp. 137-142. http://geodesic.mathdoc.fr/item/VYURU_2015_8_1_a11/

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