B-Coercive Convolution Equations in Weighted Function Spaces and Their Applications
- 26 Downloads
We study the properties of B-separability for elliptic convolution operators in weighted Besov spaces and establish sharp estimates for the resolvents of the convolution operators. As a result, it is shown that these operators are positive and, in addition, play the role of negative generators of analytic semigroups. Moreover, the maximal B-regularity properties are established for the Cauchy problem for a parabolic convolution equation. Finally, these results are applied to obtain the maximal regularity properties for anisotropic integrodifferential equations and a system of infinitely many convolution equations.
Unable to display preview. Download preview PDF.
- 1.R. P. Agarwal, R. Bohner, and V. B. Shakhmurov, “Maximal regular boundary-value problems in Banach-valued weighted spaces,” Bound. Value Probl., 1, 9–42 (2005).Google Scholar
- 2.H. Amann, Linear and Quasi-Linear Equations, Vol. 1, Birkhäuser (1995).Google Scholar
- 7.O. V. Besov, V. P. Il’in, and S. M. Nikolskii, Integral Representations of Functions and Embedding Theorems [in Russian], Nauka, Moscow (1975).Google Scholar
- 8.C. Bota, B. Caruntu, and C. Lazureanu, The least square homotopy perturbation method for boundary value problems,” Appl. Comput. Math., 16, No. 1, 39–47 (2017).Google Scholar
- 16.V. Poblete, “Solutions of second-order integro-differential equations on periodic Besov spaces,” Proc. Edinburgh Math. Soc. (2), 50, No. 2, 477–492 (2007).Google Scholar
- 19.V. B. Shakmurov, “Embedding operators in vector-valued weighted Besov spaces and applications,” J. Funct. Spaces Appl., 2012 (2012).Google Scholar
- 20.V. B. Shakhmurov, “Embedding theorems in Banach-valued B-spaces and maximal B-regular differential operator equations,” J. Inequal. Appl., 1–22 (2006).Google Scholar
- 25.H. Triebel, Interpolation Theory. Function Spaces. Differential Operators, North-Holland, Amsterdam (1978.)Google Scholar
- 28.S. Yakubov and Ya. Yakubov, Differential-Operator Equations. Ordinary and Partial Differential Equations, Chapmen & Hall /CRC, Boca Raton (2000).Google Scholar