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.
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
\Bibitem{SagRas15}
\by M.~A.~Sagadeeva, A.~S.~Rashid
\paper Existence of solutions in quasi-Banach spaces for evolutionary Sobolev type equations in relatively radial case
\jour J. Comp. Eng. Math.
\yr 2015
\vol 2
\issue 2
\pages 71--81
\mathnet{http://mi.mathnet.ru/jcem7}
\crossref{https://doi.org/10.14529/jcem150207}
\elib{https://elibrary.ru/item.asp?id=23885337}
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https://www.mathnet.ru/eng/jcem7
https://www.mathnet.ru/eng/jcem/v2/i2/p71
This publication is cited in the following 3 articles:
A. V. Keller, “O napravleniyakh issledovanii uravnenii sobolevskogo tipa”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 16:4 (2023), 5–32
F. L. Hasan, “The bounded solutions on a semiaxis for the linearized Hoff equation in quasi-Sobolev spaces”, J. Comp. Eng. Math., 4:1 (2017), 27–37
F. L. Hasan, “Solvability of initial problems for one class of dynamical equations in quasi-Sobolev spaces”, J. Comp. Eng. Math., 2:3 (2015), 34–42
Citation in format AMSBIB
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