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2022, vol. 26, br. 1, str. 89-101
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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-adresa: ferreirajorge2012@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.
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