Identifications for General Degenerate Problems of Hyperbolic Type in Hilbert Spaces
- Authors: Favini A1, Marinoschi G2, Tanabe H3, Yakubov Y.4
-
Affiliations:
- Universita` di Bologna
- Institute of Statistical Mathematics and Applied Mathematics
- Hirai Sanso
- Tel-Aviv University
- Issue: Vol 64, No 1 (2018): Differential and Functional Differential Equations
- Pages: 194-210
- Section: New Results
- URL: https://journals.rudn.ru/CMFD/article/view/22269
- DOI: https://doi.org/10.22363/2413-3639-2018-64-1-194-210
Cite item
Full Text
Abstract
In a Hilbert space X, we consider the abstract problem M∗ddt(My(t))=Ly(t)+f(t)z,0≤t≤τ,My(0)=My0, where L is a closed linear operator in X and M∈L(X) is not necessarily invertible, z∈X. Given the additional information Φ[My(t)]=g(t) wuth Φ∈X∗, g∈C1([0,τ];C). We are concerned with the determination of the conditions under which we can identify f∈C([0,τ];C) such that y be a strict solution to the abstract problem, i.e., My∈C1([0,τ];X), Ly∈C([0,τ];X). A similar problem is considered for general second order equations in time. Various examples of these general problems are given.
About the authors
A Favini
Universita` di Bologna
Email: angelo.favini@unibo.it
G Marinoschi
Institute of Statistical Mathematics and Applied Mathematics
Email: gabimarinoschi@yahoo.com
H Tanabe
Hirai Sanso
Email: h7tanabe@jttk.zaq.ne.jp
Ya Yakubov
Tel-Aviv University
Email: yakubov@post.tau.ac.il
References
- Engel K.-J., Nagel R. One-parameter semigroups for linear evolution equations. - Berlin: Springer, 2000.
- Favini A., Marinoschi G. Identification for degenerate problems of hyperbolic type// Appl. Anal. - 2012. - 91, № 8. - С. 1511-1527.
- Favini A., Marinoschi G. Identification for general degenerate problems of hyperbolic type// Bruno Pini Math. Anal. Semin. Univ. Bologna - 2016. - 7. - С. 175-188.
- Favini A., Yagi A. Degenerate differential equations in Banach spaces. - New York: Marcel Dekker, 1999.
- Lorenzi A. An introduction to identification problems via functional analysis. - Berlin: De Gruyter, 2001.
- Pazy A. Semigroup of linear operators and applications to partial differential equations. - New York: Springer-Verlag, 1983.
