Previous |  Up |  Next


Title: Stability in nonlinear evolution problems by means of fixed point theorems (English)
Author: Koliha, J. J.
Author: Straškraba, Ivan
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 38
Issue: 1
Year: 1997
Pages: 37-59
Category: math
Summary: The stabilization of solutions to an abstract differential equation is investigated. The initial value problem is considered in the form of an integral equation. The equation is solved by means of the Banach contraction mapping theorem or the Schauder fixed point theorem in the space of functions decreasing to zero at an appropriate rate. Stable manifolds for singular perturbation problems are compared with each other. A possible application is illustrated on an initial-boundary-value problem for a parabolic equation in several space variables. (English)
Keyword: evolution equations
Keyword: stabilization of solutions
Keyword: parabolic problem
MSC: 34C30
MSC: 34D15
MSC: 34G20
MSC: 35B40
MSC: 35K20
MSC: 35K99
MSC: 47H20
MSC: 47N20
idZBL: Zbl 0891.34065
idMR: MR1455469
Date available: 2009-01-08T18:29:00Z
Last updated: 2012-04-30
Stable URL:
Reference: [1] Appel J., Zabrejko P.P.: Nonlinear Superposition Operators.Cambridge University Press, Cambridge, 1990. MR 1066204
Reference: [2] Crandall M., Liggett T.: Generation of semigroups of nonlinear transformations on general Banach spaces.Amer. J. Math. 93 (1977), 265-298. MR 0287357
Reference: [3] Hale J.K.: Theory of Functional Differential Equations.Springer, New York, 1977. Zbl 1092.34500, MR 0508721
Reference: [4] Hale J.K.: Asymptotic Behavior of Dissipative Systems.Mathematical Surveys and Monographs No. 25, Amer. Math. Soc., Providence, 1988. Zbl 0642.58013, MR 0941371
Reference: [5] Iwamiya T., Takahashi T., Oharu T.: Characterization of nonlinearly perturbed Functional Analysis and Related Topics, Proceedings, Kyoto 1991, H. Komatsu (ed.), Lecture Notes in Math. No. 1540, Springer, New York, 1993. Zbl 0819.47081
Reference: [6] Komatsu H.: Fractional powers of generators, II Interpolation spaces.Pacific J. Math. 21 (1967), 89-111. MR 0206716
Reference: [7] Krasnosel'skij M.A., Zabrejko P.P., Pustyl'nik E.I., Sobolevskij P.E.: Integral Operators in the Spaces of Integrable Functions (in Russian).Nauka, Moscow, 1966.
Reference: [8] Krein M., Dalecki J.: Stability of the Solutions of Differential Equations in Banach Spaces.Amer. Math. Soc., Providence, 1974. MR 0352639
Reference: [9] Lunardi A.: Analytic Semigroups and Optimal Regularity in Parabolic Problems.Birkhäuser, Basel, 1995. Zbl 0816.35001, MR 1329547
Reference: [10] Pazy A.: Semigroups of Linear Operators and Applications to Partial Differential Equations.Springer, New York, 1983. Zbl 0516.47023, MR 0710486
Reference: [11] Rauch J.: Stability of motion for semilinear Boundary Value Problems for Linear Evolution Partial Differential Equations, Proceedings of the NATO Advanced Study Institute held in Liège, Belgium, September 6-17, 1976, H. G. Garnir (ed.), NATO Advanced Study Institute Series C, Mathematical and Physical Sciences, vol. 29, Reidel Publishing Co., Dordrecht, 1977. Zbl 0347.35015, MR 0492677
Reference: [12] Tanabe H.: Equations of Evolution.Pitman, London, 1979. Zbl 0417.35003, MR 0533824


Files Size Format View
CommentatMathUnivCarolRetro_38-1997-1_4.pdf 310.8Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo