Decay estimates for the time-fractional evolution equations with time-dependent coefficients
Smadiyeva A.G. Torebek B.T.
30 August 2023Royal Society Publishing
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
2023#479Issue 2276
In this paper, the initial-boundary value problems for the time-fractional degenerate evolution equations are considered. Firstly, in the linear case, we obtain the optimal rates of decay estimates of the solutions. The decay estimates are also established for the time-fractional evolution equations with nonlinear operators such as: p-Laplacian, the porous medium operator, degenerate operator, mean curvature operator and Kirchhoff operator. At the end, some applications of the obtained results are given to derive the decay estimates of global solutions for the time-fractional Fisher-KPP-type equation and the time-fractional porous medium equation with the nonlinear source.
Caputo derivative , decay estimate , Kilbas-Saigo function , sub-diffusion equation
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Al-Farabi Kazakh National University, Al-Farabi, ave. 71, Almaty, 050040, Kazakhstan
Institute of Mathematics and Mathematical Modeling, 125 Pushkin str., Almaty, 050010, Kazakhstan
Department of Mathematics: Analysis Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, Ghent, Belgium
Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling
Department of Mathematics: Analysis Logic and Discrete Mathematics
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