Abstract
We obtain a criterion for invertibility in Hölder spaces of linear parabolic operators of arbitrary order with any number of spatial variables and almost-periodic coefficients.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
V. V. Zhikov, “Several problems of admissibility and dichotomy. The averaging principle,” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 40 (1976), 1380–1408.
S. D. Éidel'man, Parabolic Systems [in Russian], Nauka, Moscow, 1964.
V. B. Levenshtam, “Averaging of quasilinear parabolic equations with a rapidly oscillating principal part. Exponential dichotomy,” Izv. Ross. Akad. Nauk Ser. Mat. [Russian Acad. Sci. Izv. Math.], 56 (1992), no. 4, 813–851.
J. Massera and J. Schäffer, Linear Differential Equations and Function Spaces, Academic Press, New York, 1970.
Yu. L. Daletskii and M. G. Krein, Stability of Solutions of Differential Equations in the Banach space [in Russian], Nauka, Moscow, 1970.
M. A. Krasnosel'skii, V. Sh. Burd, and Yu. S. Kolesov, Nonlinear Almost-Periodic Oscillations [in Russian], Nauka, Moscow, 1970.
É. Mukhamadiev, “Invertibility of differential operators in the space of bounded and continuous functions,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 196 (1971), no. 1, 47–49.
V. V. Zhikov and V. M. Tyurin, “On invertibility of the operator d/dt + A(t) in the space of bounded functions,” Mat. Zametki [Math. Notes], 19 (1976), no. 1, 99–104.
D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer-Verlag, Heidelberg, 1981.
V. M. Tyurin, “Invertibility of linear differential operators in some function spaces,” Sibirsk. Mat. Zh. [Siberian Math. J.], 32 (1991), no. 3, 160–165.
A. G. Baskakov, “Semigroups of difference operators in the spectral analysis of linear differential operators,” Funktsional. Anal. i Prilozhen. [Functional Anal. Appl.], 30 (1996), no. 3, 1–11.
B. M. Levitan and V. V. Zhikov, Almost-Periodic Functions and Differential Equations [in Russian], Izd-vo Moskov. Gos. Univ., Moscow, 1978.
L. Bers, F. John, and M. Schechter, Partial Differential Equations, Interscience, New York, 1964.
M. A. Shubin, “Almost-periodic functions and partial differential operators,” Uspekhi Mat. Nauk [Russian Math. Surveys], 33 (1978), no. 2, 3–47.
B. P. Demidovich, Lectures on Mathematical Theory of Stability [in Russian], Nauka, Moscow, 1967.
J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites nonlinéaires, Dunod, Paris, 1969.
V. V. Zhikov, S. M. Kozlov, and O. A. Oleinik, “On the G-convergence of parabolic operators,” Uspekhi Mat. Nauk [Russian Math. Surveys], 36 (1981), no. 1, 11–58.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Levenshtam, V.B. Unique Solvability of Parabolic Equations with Almost-Periodic Coefficients in Hölder Spaces. Mathematical Notes 73, 813–828 (2003). https://doi.org/10.1023/A:1024001930334
Issue Date:
DOI: https://doi.org/10.1023/A:1024001930334