Sturm-Liouville abstract problems for the second order differential equations in a non commutative case
Автор: Kaid M., Ould Melha K.
Рубрика: Математическое моделирование
Статья в выпуске: 3 т.11, 2018 года.
Бесплатный доступ
In this paper we prove some new results on Sturm - Liouville abstract problems of the second order differential equations of elliptic type in a new non-commutative framework. We study the case when the second member belongs to a Sobolov space. Existence, uniqueness and optimal regularity of the strict solution are proved. This paper is naturally the continuation of the ones studied by Cheggag et al in the commutative case. We also give an example to which our theory applies.
Second-order abstract elliptic differential equations, sturm - liouville boundary conditions in non commutative cases, analytic semigroup, maximal regularity
Короткий адрес: https://sciup.org/147232898
IDR: 147232898 | DOI: 10.14529/mmp180304
Список литературы Sturm-Liouville abstract problems for the second order differential equations in a non commutative case
- Cheggag M., Favini A., Labbas R., Maingot S., Medeghri A. Sturm-Liouville Problems for an Abstract Differential Equation of Elliptic Type in UMD Spaces. Differential and Integral Equations, 2008, vol. 21, no. 9-10, pp. 981-1000.
- Cheggag M., Favini A., Labbas R., Maingot S., Medeghri A. Abstract Differential Equations of Elliptic Type with General Robin Boundary Conditions in Hölder Spaces. Applicable Analysis: an International Journal, 2012, vol. 91, no. 8, pp. 1453-1475.
- Cheggag M., Favini A., Labbas R., Maingot S., Ould Melha K. New Results on Complete Elliptic Equations with Robin Boundary Coefficient-Operator Conditions in Non Commutative Case. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2017, vol. 10, no. 1, pp. 70-96. DOI: 10.14529/mmp170105
- Dore G., Yakubov S. Semigroup Estimates and Noncoercive Boundady Value Problems. Semigroups Forum, 2000, no. 60, pp. 93-121.
- Lunardi A. Analytic Semigroups and Optimal Regularity in Parabolic Problems. Basel, Birkhaüser, 1995.
- Grisvard P. Spazi di tracce ed applicazioni. Rendiconti di Matematica. Serie VI, 1972, vol. 5, pp. 657-729. (in Italian)
- Cheggag M., Favini A., Labbas R., Maingot S., Medeghri A. Elliptic Problems with Robin Boundary Coefficient-Operator Conditions in General Lp Sobolev Spaces and Applications. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2015, vol. 8, no. 3, pp. 56-77.
- DOI: 10.14529/mmp150304
- Prüss J., Sohr H. On Operators with Bounded Imaginary Powers in Banach Spaces. Mathematische zeitschrift, 1990, vol. 203, no. 3, pp. 429-452.
- Grisvard P. Commutativité de deux foncteurs d'interpolation et applications. Journal de mathématiques pures et appliquées, 1966, no. 45, pp. 143-290.
- Triebel H. Interpolation Theory, Functions Spaces, Differential Operators. Amsterdam, N.Y., Oxford, North-Holland, 1978.
- Favini A., Labbas R., Maingot S., Tanabe H., Yagi A. A Simplified Approach in the Study of Elliptic Differential Equation in UMD Space and New Applications. Funkcialaj ekvacioj, 2008, vol. 51, no. 2, pp. 165-187.
- Dore G., Venni A. On the Closedness of the Sum of Tow Closed Operators. Mathematische zeitschrift, 1987, vol. 196, no. 2, pp. 189-201.
- DOI: 10.1007/BF01163654
- Favini A., Labbas R., Maingot S., Tanabe H., Yagi A. Complete Abstract Differential Equation of Elliptic Type in U.M.D Spaces. Funkcialaj ekvacioj, 2006, vol. 49, no. 2, pp. 193-214.
