| Title:
|
Inverse problem for semilinear ultraparabolic equation of higher order (English) |
| Author:
|
Protsakh, Nataliya |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
140 |
| Issue:
|
4 |
| Year:
|
2015 |
| Pages:
|
395-404 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the existence and the uniqueness of the weak solution of an inverse problem for a semilinear higher order ultraparabolic equation with Lipschitz nonlinearity. The main aim is to determine the weak solution of the equation and some functions that depend on the time variable, appearing on the right-hand side of the equation. The overdetermination conditions introduced are of integral type. In order to prove the solvability of this problem in Sobolev spaces we use the Galerkin method and the method of successive approximations. (English) |
| Keyword:
|
ultraparabolic equation |
| Keyword:
|
mixed problem |
| Keyword:
|
inverse problem |
| Keyword:
|
weak solution |
| MSC:
|
35K70 |
| MSC:
|
35R30 |
| idZBL:
|
Zbl 06537672 |
| idMR:
|
MR3432541 |
| DOI:
|
10.21136/MB.2015.144458 |
| . |
| Date available:
|
2015-11-17T20:44:07Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144458 |
| . |
| Reference:
|
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| Reference:
|
[2] Gajewski, H., Gröger, K., Zacharias, K.: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen.Mathematische Lehrbücher und Monographien, II. Abteilung, Mathematische Monographien 38 Akademie, Berlin German (1974). MR 0636412 |
| Reference:
|
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| Reference:
|
[4] Kamynin, V. L.: On the inverse problem of determining the right-hand side of a parabolic equation under an integral overdetermination condition.Math. Notes 77 (2005), 482-493 translated from Matematicheskie Zametki 77 (2005), 522-534. Zbl 1075.35106, MR 2178019, 10.1007/s11006-005-0047-6 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[7] Lanconelli, E., Pascucci, A., Polidoro, S.: Linear and nonlinear ultraparabolic equations of Kolmogorov type arising in diffusion theory and in finance.Nonlinear Problems in Mathematical Physics and Related Topics II. In honour of Professor O. A. Ladyzhenskaya Int. Math. Ser. (N. Y.) 2 Kluwer Academic Publishers, New York (2002), 243-265 M. S. Birman et al. Zbl 1032.35114, MR 1972000 |
| Reference:
|
[8] Lavrenyuk, S., Protsakh, N.: Boundary value problem for nonlinear ultraparabolic equation in unbounded and with respect to time variable domain.Tatra Mt. Math. Publ. 38 (2007), 131-146. MR 2428919 |
| Reference:
|
[9] Lavrenyuk, S. P., Protsakh, N. P.: Mixed problem for a nonlinear ultraparabolic equation that generalizes the diffusion equation with inertia.Ukr. Mat. Zh. 58 (2006), 1192-1210 Ukrainian translation in Ukr. Math. J. 58 (2006), 1347-1368. Zbl 1114.35112, MR 2345088, 10.1007/s11253-006-0137-y |
| Reference:
|
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| Reference:
|
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| . |
