Inverse problem for semilinear ultraparabolic equation of higher order

Nataliya Protsakh

Mathematica Bohemica (2015)

  • Volume: 140, Issue: 4, page 395-404
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Protsakh, Nataliya. "Inverse problem for semilinear ultraparabolic equation of higher order." Mathematica Bohemica 140.4 (2015): 395-404. <http://eudml.org/doc/271803>.

@article{Protsakh2015,
abstract = {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.},
author = {Protsakh, Nataliya},
journal = {Mathematica Bohemica},
keywords = {ultraparabolic equation; mixed problem; inverse problem; weak solution},
language = {eng},
number = {4},
pages = {395-404},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Inverse problem for semilinear ultraparabolic equation of higher order},
url = {http://eudml.org/doc/271803},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Protsakh, Nataliya
TI - Inverse problem for semilinear ultraparabolic equation of higher order
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 4
SP - 395
EP - 404
AB - 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.
LA - eng
KW - ultraparabolic equation; mixed problem; inverse problem; weak solution
UR - http://eudml.org/doc/271803
ER -

References

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  2. Gajewski, H., Gröger, K., Zacharias, K., Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Mathematische Lehrbücher und Monographien, II. Abteilung, Mathematische Monographien 38 Akademie, Berlin German (1974). (1974) MR0636412
  3. Ivanchov, M., Inverse Problems for Equations of Parabolic Type, Mathematical Studies, Monograph Series 10 VNTL Publishers, L'viv (2003). (2003) Zbl1147.35110MR2406459
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  5. Kolmogoroff, A., Zufällige Bewegungen (zur Theorie der Brownschen Bewegung), Ann. Math. (2) 35 German (1934), 116-117. (1934) Zbl0008.39906MR1503147
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  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. (2002) Zbl1032.35114MR1972000
  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. (2007) MR2428919
  9. Lavrenyuk, S. P., Protsakh, N. P., 10.1007/s11253-006-0137-y, Ukr. Mat. Zh. 58 (2006), 1192-1210 Ukrainian translation in Ukr. Math. J. 58 (2006), 1347-1368. (2006) Zbl1114.35112MR2345088DOI10.1007/s11253-006-0137-y
  10. Protsakh, N., Inverse problem for an ultraparabolic equation, Tatra Mt. Math. Publ. 54 (2013), 133-151. (2013) MR3099656
  11. Safiullova, R. R., On solvability of the linear inverse problem with unknown composite right-hand side in hyperbolic equation, Vestn. Yuzhno-Ural. Gos. Univ., Ser. Mat. Model. Program. 27 Russian (2009), 93-105. (2009) Zbl1192.35189

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