Decay estimates for evolution equations with classical and fractional time-derivatives

Elisa Affili; Enrico Valdinoci

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arXiv · 1807.10041

Decay estimates for evolution equations with classical and fractional time-derivatives

Elisa Affili·Enrico Valdinoci

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Abstract

Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving both standard and Caputo time-derivative, complex valued magnetic operators, fractional porous media equations and nonlocal Kirchhoff operators. Both local and fractional space diffusion are taken into account, possibly in a nonlinear setting. The different quantitative behaviors, which distinguish polynomial decays from exponential ones, depend heavily on the structure of the time-derivative involved in the equation.

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Elisa Affili, Enrico Valdinoci. 2018-07-26. Decay estimates for evolution equations with classical and fractional time-derivatives. https://arxiv.org/abs/1807.10041

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