This article is cited in 1 paper

Short Notes

On one Sobolev type mathematical model in quasi-Banach spaces

A. A. Zamyshlyaeva, H. M. Al Helli

South Ural State University, Chelyabinsk, Russian Federation

Abstract: 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.

UDC: 517.9

MSC: 46A16, 35G05

Received: 04.09.2014

Language: English

DOI: 10.14529/mmp150112

Bibliographic databases:

• 
•