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DOI:

https://doi.org/10.12775/TMNA.2021.015

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M. Allen, L. Caffarelli and A. Vasseur, Porous medium flow with both a fractional potential pressure and fractional time derivative, Chin. Ann. Math.Ser. B 38 (2017), 45–82.

A. Bekkai, B. Rebiai and M. Kirane, On local existence and blowup of solutions for a time-space fractional diffusion equation with exponential nonlinearity, Math. Meth. Appl. Sci. (2019), 1–12.

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E. Dinezza, G. Palatucci and E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces, Bull. Sci. Math. 136 (2012), 521–573.

S.D. Eidelman and A.N. Kochubei, Cauchy problem for fractional diffusion equations, J. Differential Equations 199 (2004), 211–255.

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H. Fujita, On the blowing up of solutions of the Cauchy problem for ut = ∆u + uα+1 , J. Fac. Sci. Univ. Tokyo Sect. I 13 (1966), 109–124.

H. Han and Z. Wang, An alternating direction implicit scheme of a fractional-order diffusion tensor image registration model, Appl. Math. Comput. 356 (2019), 105–118.

K. Hayakawa, On nonexistence of global solutions of some semilinear parabolic equations, Proc. Japan Acad. 49 (1973), 503–505.

J.X. Jia and K.X. Li, Maximum principles for a time space fractional diffusion equation, Appl. Math. Lett. 62 (2016), 23–28.

J.X. Jia, J.G. Peng and J.Q. Yang, Harnack’s inequality for a space-time fractional diffusion equation and applications to an inverse source problem, J. Differential Equations 262 (2017), 4415–4450.

J. Kemppainen, J. Siljander and R. Zacher, Representation of solutions and largetime behavior for fully nonlocal diffusion equations, J. Differential Equations 263 (2017), 149–201.

A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science Limited, 2006.

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V.N. Kolokoltsov and M.A. Veretennikov, Well-posedness and regularity of the Cauchy problem for nonlinear fractional in time and space equations, Fract. Differ. Calc. 4 (2014), 1–30.

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E. Nane, Fractional Cauchy Problems on Bounded Domains: Survey of Recent Results, Fractional Dynamics and Control, Springer, 2012.

R. Servadei and E. Valdinoci, Variational methods for non-local operators of elliptic type, Discrete Contin. Dyn. System 33 (2013), 2015–2137.

L. Silvestre, Regularity of the obstacle problem for a fractional power of the laplace operator, Comm. Pure Appl. Math. 60 (2007), 67–112.

J.L. Vázquez, Recent progress in the theory of nonlinear diffusion with fractional laplacian operators, Discrete Contin. Dyn. Syst. Ser. S 7 (2014), 857–885.

M.Q. Xiang, V.D. Rădulescu and B.L. Zhang, Nonlocal Kirchhoff diffusion problems: local existence and blow-up of solutions, Nonlinearity 31 (2018), 3228–3250.

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Q.G. Zhang, H.R. Sun and Y.N. Li, Global existence and blow-up of solutions of the Cauchy problem for a time fractional diffusion system, Comput. Math. Appl. 78 (2019), 1357–1366.

Opublikowane

2022-09-13

Jak cytować

1.
& . Topological Methods in Nonlinear Analysis [online]. 13 wrzesień 2022, T. 60, nr 2, s. 415–440. [udostępniono 3.7.2024]. DOI 10.12775/TMNA.2021.015.

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