The spaces of initial data are described in terms of Besov spaces.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, the weak and strong solvability of the second boundary-value problem for a parabolic differential-difference equation is considered in spaces like Lp(0, T; X).
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Key Findings & Data:In this paper, the weak and strong solvability of the second boundary-value problem for a parabolic differential-difference equation is considered in spaces like Lp(0, T; X).
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Conclusion & Impact:The spaces of initial data are described in terms of Besov spaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this paper, the weak and strong solvability of the second boundary-value problem for a parabolic differential-difference equation is considered in spaces like Lp(0, T; X). The spaces of initial data are described in terms of Besov spaces.
Özet
Bu makalede parabolik diferensiyel-fark denklemi için ikinci sınır- değer probleminin zayıf ve güçlü çözülebilirliği Lp(0, T; X) gibi uzaylarda ele alınmıştır. Başlangıç değer uzayları Besov uzayları kullanılarak ifade edilmiştir.
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Cite This Article
SELİTSKİİ, A. M. (2022). Lp uzayında parabolik diferensiyel-fark denklemi için ikinci sınır-değer probleminin zayıf ve güçlü çözülebilirliği. Contemporary Analysis and Applied Mathematics, Cilt: 2 - Sayı: 2, 224–229. https://ajindex.com/articles/476469
1] M. S. Agranovich, A. M. Selitskii, Fractional powers of operators corresponding to coercitive problems in Lipschitz domains, Funktsionalnyi Analiz i Ego Prilozheniya 47 (2) (2013) 217, English transl. in: Funct. Anal. Appl. 47 (2) (2013) 8395. [2] A. Ashyralyev, P. E. Sobolevskii, Well-Posedness of Parabolic Difference Equations, Birkh¨auser, Basel, 1994. [3] O. V. Besov, Investigation of a class of function spaces in connection with imbedding and extension theorems, Trudy Mat. Inst. Steklov. 60 (1961) 4281 (in Russian). [4] R. Dautray, J.-L. Lions, Analyse Math´ematique et Calcul Num´erique t. 3., MASSON, Paris, 1985. [5] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1995. [6] E. M. Ouhabaz, Analysis of Heat Equations on Domains, Princeton Univ. Press, Princeton and Oxford, 2005. [7] V. S. Rychkov, On restrictions and extensions of the Besov and TribelLizorkin spaces with respect to Lipschitz domains, J. London Math. Soc. 60 (2) (1997) 237257. [8] A. M. Selitskii, The space of initial data of the second boundary-value problem for parabolic differential-difference equation, Contemporary Analysis and Applied Mathematics 1 (1) (2013)3441. [9] A. M. Selitskii, The space of initial data of the Robin boundary-value problem for parabolic differential-difference equations, Contemporary Analysis and Applied Mathematics 1 (2) (2013) 9197. [10] A. M. Selitskii, A. L. Skubachevskii, The second boundary-value problem for parabolic differentialdifference equations, Trudy Seminara I.G. Petrovskogo. 26 (2007) 323346, English transl. in: J. Math. Sci. 143 (4) (2007) 33863400. [11] H. Triebel, Interpolation Theory, Functional Spaces, Differential Operators, VEB Deutscher Verlag der Wissenschaften, Berlin, 1978.