Abstract:
The Sobolev type equations are
studied quite complete in Banach spaces. Quasi-Sobolev spaces are quasi normalized complete spaces of sequences. Recently the Sobolev type equations began to be studied in these
spaces. The paper is devoted to the study of boundary on axis
solutions for the Barenblatt–Zheltov–Kochina model.
Apart the introdsction and bibliograthy the paper contain two parts. In the first one gives preliminary information about the properties of operators in quasi Banach spaces, as well as about the relatively bounded operator. The second part gives main result of the paper about boundary on axis solutions for the Barenblatt–Zheltov–Kochina model in quasi-Sobolev spaces.
Note that reference list reflects the tastes of the author
and can be supplemented.
Keywords:
Sobolev type equation; spaces of sequances; Laplase quasi-operator; Grin function; analogue of Barenblatt–Zheltov–Kochina model.
Citation:
M. A. Sagadeeva, F. L. Hasan, “Bounded solutions of Barenblatt–Zheltov–Kochina model in quasi-Sobolev spaces”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 8:4 (2015), 138–144
This publication is cited in the following 6 articles:
Sophiya A. Zagrebina, Natalya N. Solovyova, Springer Proceedings in Mathematics & Statistics, 325, Semigroups of Operators – Theory and Applications, 2020, 95
A. A. Bayazitova, “Ob obobschennoi kraevoi zadache dlya lineinykh uravnenii sobolevskogo tipa na grafe”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 10:3 (2018), 5–11
D. E. Shafranov, N. V. Adukova, “Solvability of the Showalter–Sidorov problem for Sobolev type equations with operators in the form of first-order polynomials from the Laplace–Beltrami operator on differential forms”, J. Comp. Eng. Math., 4:3 (2017), 27–34
M. A. Sagadeeva, “Mathematical bases of optimal measurements theory in nonstationary case”, J. Comp. Eng. Math., 3:3 (2016), 19–32
N. A. Manakova, “On modified method of multistep coordinate descent for optimal control problem for semilinear Sobolev-type model”, J. Comp. Eng. Math., 3:4 (2016), 59–72