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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
Adams, R.A. (1975) Sobolev Spaces. Academic Press
Carracedo, C., Sanz, A.M. (2001) The theory of Fractional powers of operators. Amsterdam: Elsevier
Cholewa, J.W., Dlotko, T. (2000) Global attractors in abstract parabolic problems. Cambridge: Cambridge University Press
Córdoba, A., Córdoba, D. (2004) A maximum principle applied to quasi-geostrophic equations. Communications in Mathematical Physics, 249(3): 97-108
Droniou, J., Imbert, C. (2006) Fractal first order partial diferential equations. Archive for Rational Mechanics and Analysis, 182: 299-331
Henry, D. (1981) Geometric theory of semilinear parabolic equations. Berlin: Springer-Verlag
Henry, D.B. (1982) How to remember the Sobolev inequalities. u: Guedes de Figueiredo, D.; Hönig, C.S. [ur.] Lecture notes in mathematics, Berlin-Heidelberg: Springer Berlin Heidelberg, 957: 97-109
Ju, N. (2005) The maximum principle and the global attractor for the dissipative 2d quasi-geostrophic equations. Communications in Mathematical Physics, 255(1): 161-181
Kato, T. (1980) Perturbation theory for semigroups of operators. Berlin: Springer, 477-513
Komatsu, H. (1966) Fractional powers of operators. Pacific Journal of Mathematics, 19(2): 285-346
Komatsu, H. (1967) Fractional powers of operators. II. Interpolation spaces. Pacific Journal of Mathematics, 21(1): 89-111
Musina, R., Nazarov, A.I. (2015) On fractional Laplacians. Revista Matemática Iberoamericana, 32(1): 257-266
Samko, S.G., Kilbas, A.A., Marichev, O.I. (1993) Fractional integrals and derivatives: Theory and applications. Yverdon: Gordon and Breach
Yosida, K. (1979) Functional analysis. 101
 

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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