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2022, vol. 26, br. 1, str. 89-101
Global and local existence of solution for fractional heat equation in R N by Balakrishnan definition
(naslov ne postoji na srpskom)
aFederal Fluminense University, Department of Exact Sciences, Volta Redonda, Brazil
bDicle University, Department of Mathematics, Diyarbakır, Turkey
cJahrom University, Department of Mathematics, Jahrom, Iran
dFederal University of Pará, Faculty of Exact Sciences and Technology, Pará, Brazil
eFederal University of Pará Augusto, Institute of Exact and Natural Sciences, Belém, Brazil

e-adresaferreirajorge2012@gmail.com, episkin@dicle.edu.tr, mshahrouzi@jahromu.ac.ir, sebastiao@ufpa.br, danielvrocha2011@gmail.com
Ključne reči: Fractional powers of operator; Balakrishinan; global solvability; Heat Equation
Sažetak
(ne postoji na srpskom)
Our aim here is to collect and to compare two definitions of the fractional powers of non-negative operators that can be found in the literature; we will present the proof of an equivalence and compare properties of that notions in different approaches. Then we will apply next this equivalence in the study of global and local existence of solution for the semilinear Cauchy problem in R N with fractional Laplacian ut = -(-∆)au + f(x, u), u(0, x) = u0(x), x ∈ R N.
Reference
Novododat članak: provera, normiranje i linkovanje referenci u toku.
J. W. Cholewa, T. Dlotko, Global Attractors in Abstract Parabolic Problems, Cambridge University Press, Cambridge, 2000.
A. Cordoba, D. Cordoba, A Maximum Principle applied to quasi-geostrophic equations, Communications in Mathematical Physics, 249 (2004), 97-108.
D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer-Verlag, Berlin, 1981.
J. Droniou, C. Imbert, Fractal first order partial diferential equations, Archive for Rational Mechanics and Analysis, 182 (2006), 299-331.
T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1980.
H. Komatsu, Fractional powers of operators, Pacific Journal of Mathematics, 19 (1966), 285-346.
H. Komatsu, Fractional powers of operators, II. Interpolation spaces, Pacific Journal of Mathematics, 21 (1967), 89-111.
C. Martínez Carracedo, M. Sanz Alix, The Theory of Fractional Powers of Operators, Elsevier, Amsterdam, 2001.
S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, 1993.
K. Yosida, Functional Analysis (Fifth Edition), Springer-Verlag, Berlin, 1979.
D. B. Henry, How to remember the Sobolev inequalities. In: Guedes de Figueiredo D., Hönig C.S. (eds) Differential Equations. Lecture Notes in Mathematics, Vol. 957, Springer, Berlin, Heidelberg, 1982.
N. Ju, The maximum principle and the global attractor for the dissipative 2D quasigeostrophic equations, Communications in Mathematical Physics, 255 (2005), 161-181.
R. A. Adams, Sobolev Spaces, Academic Press, 1975.
R. Musina, A. I. Nazarov, On fractional Laplacians, arXiv, 2015.
 

O članku

jezik rada: engleski
vrsta rada: neklasifikovan
DOI: 10.5937/MatMor2201089F
primljen: 31.10.2021.
revidiran: 01.12.2021.
prihvaćen: 17.12.2021.
objavljen onlajn: 03.02.2022.
objavljen u SCIndeksu: 25.06.2022.
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