| Title | Parabolic mixed problems in spaces of generalized smoothness |
| Publication Type | Journal Article |
| Year of Publication | 2014 |
| Authors | Los, VN, Murach, AA |
| Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
| DOI | 10.15407/dopovidi2014.06.023 |
| Issue | 6 |
| Section | Mathematics |
| Pagination | 23-31 |
| Date Published | 6/2014 |
| Language | Russian |
| Abstract | We prove theorems on a well-posedness of a general parabolic initial-boundary-value problem in some classes of Hilbert spaces of generalized smoothness. The latter is characterized by number parameters and a supplementary function parameter that varies slowly at infinity in Karamata's sense. As an application, we give new sufficient conditions under which some generalized derivatives of a solution to the problem should be continuous. |
| Keywords | generalized smoothness, parabolic mixed problems, spaces |
1. Agranovich M. S., Vishik M. I. Uspekhi mat. nauk, 1964, 19, No. 3: 53–161 (in Russian).
2. Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva n. N. Linear and quasilinear equations of parabolic type. Moscow: Nauka, 1967. (in Russian).
3. Lions J.-L., Magenes E. Non-homogeneous boundary-value problems and applications. Vol. 2. Berlin: Springer, 1972.
4. Zhytarashu N. V., Eidelman S. D. Parabolic boundary value problems. Kishinev: Shtiintsa, 1992 (in Russian).
5. Eidel’man S. D. Parabolic equations. In: Encycl. Math. Sci. Vol. 63. Partial differential equations, VI. Berlin: Springer, 1994: 205–316.
6. Ivasishen S. D. The Green matrices of parabolic boundary value problems. Kyiv: Vyshcha shkola, 1990 (in Russian).
7. Hörmander L. Linear partial differential operators. Berlin: Springer, 1963. https://doi.org/10.1007/978-3-642-46175-0
8. Volevich L. R., Paneyakh B. P. Uspekhi mat. nauk., 1965, 20, No. 1: 3–74 (in Russian).
9. Lizorkin P. I. Spaces of generalized smoothness. In: Triebel H. Theory of function spaces. Moscow: Mir, 1986: 381–415 (in Russian).
10. Farkas W., Leopold H.-G. Ann. Mat. Pura Appl., 2006, 185, No. 1: 1–62. https://doi.org/10.1007/s10231-004-0110-z
11. Mikhailets V. A., Murach A. A. Hörmander spaces, interpolation and elliptic problems. Kyiv: Institute of Mathematics of NAS of Ukraine, 2010. Available as arXiv: 1106.3214. (in Russian).
12. Mikhailets V. A., Murach A. A. Banach J. Math. Anal., 2012, 6, No. 2: 211–281. https://doi.org/10.15352/bjma/1342210171
13. Los V., Murach A. A. Meth. Funct. Anal. Topol., 2013, 19, No. 2: 146–160.
14. Los V. M., Murach A. A. Zb.prats Inst. of Mathematics of NAS of Ukraine, 2013, 10, No. 2: 219–234 (in Ukrainian).
15. Seneta E. Correctly changing functions. Moscow: Nauka, 1985 (in Russian).
