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This article is cited in 3 scientific papers (total in 3 papers)
Computational Mathematics
Existence of solutions in quasi-Banach spaces for evolutionary Sobolev type equations in relatively radial case
M. A. Sagadeeva, A. S. Rashid South Ural State University, Chelyabinsk, Russian Federation
Abstract:
Sobolev-type equations (equations not solved for the highest derivative) probably first appeared in the late nineteenth century. The growing recent interest in Sobolev-type equations motivates us to consider them in quasi-Banach spaces. Specifically, this study aims at understanding non-classical models of mathematical physics in quasi-Banach spaces. This paper carries over the theory of degenerate strongly continuous semigroups obtained earlier in Banach spaces to quasi-Banach spaces. We prove an analogue of the direct Hille – Yosida – Feller – Miyadera – Phillips theorem. As an application of abstract results, we consider the Showalter – Sidorov problem for modified linear Chen – Gurtin equations in quasi-Sobolev spaces.
Keywords:
degenerate strong continuous semigroups, quasi-Banach spaces, Hille – Iosida – Feller – Miadera – Phillips theorem, modified Chen – Gurtin equation, quasi-Sobolev spaces.
Received: 28.04.2015
Citation:
M. A. Sagadeeva, A. S. Rashid, “Existence of solutions in quasi-Banach spaces for evolutionary Sobolev type equations in relatively radial case”, J. Comp. Eng. Math., 2:2 (2015), 71–81
Linking options:
https://www.mathnet.ru/eng/jcem7 https://www.mathnet.ru/eng/jcem/v2/i2/p71
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