Volume 6, no. 2Pages 133 - 137
Approximations for a Degenerate C_0-semigroupM.A. Sagadeyeva, A.N. Shulepov
The results from the theory of Sobolev type equations have been actively used to measure the dynamically distorted signals recently. The formulas obtained for relatively p-radial case of Sobolev type equations are used for the numerical solution of such problems. Hille - Widder - Post approximations for the operators of strongly continuous resolving semigroup for homogeneous equations are considered in the article. The authors show that a simpler formula can be used as approximations of operators of a resolving semigroup. e consists of introduction and two parts. The information regarding the relative resolutions and theories of relatively p-radial operators are given in the first part. The approximation formulas are covered in the second part.Full text
The article consists of introduction and two parts. The information regarding the relative resolutions and theories of relatively p-radial operators are given in the first part. The approximation formulas are covered in the second part.
- Sobolev type equation, resolving semigroup of operators, Hille-Widder-Post approximations.
- 1. Favini A., Yagi A. Degenerate Differential Equations in Banach Spaces. N.Y., Basel, Hong Kong, Marcel Dekker, Inc, 1999. 236 p.
2. Pyatkov S.G. Operator Theory. Nonclassical Problems. Utrecht, Boston, Koln, Tokyo, VSP, 2002. 353 p.
3. Sviridyuk G.A., Fedorov V.E. em Linear Sobolev Type Equations and Degenerate Semigroups of Operators. Utrecht, Boston, Koln, VSP, 2003. 216 p.
4. Al'shin A.B., Korpusov M.O., Sveshnikov A.G. Blow-Up in Nonlinear Sobolev Type Equations. Berlin, de Gruyter, 2011. 648 p.
5. Shestakov A.L., Sviridyuk G.A. A New Approach to Measurement Dynamically Perturbed Signals [Novyy podkhod k izmereniyu dinamicheski iskazhennykh signalov]. Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming & Computer Software", 2010, no. 16 (192), issue 5, pp. 88-92.
6. Shestakov A.L., Keller A.V., Nazarova E.I. Numerical Solution of the Optimal Measurement Problem. Automation and Remote Control. 2012, no. 1, pp. 107-115.
7. Sviridyuk G.A. Linear Equations of Sobolev Type and Strongly Continious Semigroups of Resolving Operators with Kernels [Lineiniye uravneniya sobolevskogo tipa i sil'no nepreryvnye polugruppy razreshayushikh operatorov s yadrami]. Dokl. Akad. Nauk USSR. 1994, vol. 337, no. 5, pp. 581-584.