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arXiv · 1606.07587

Discrete maximal regularity of time-stepping schemes for fractional evolution equations

Bangti Jin·Buyang Li·Zhi Zhou
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Abstract

In this work, we establish the maximal $\ell^p$-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order $\alpha\in(0,2)$, $\alpha\neq 1$, in time. These schemes include convolution quadratures generated by backward Euler method and second-order backward difference formula, the L1 scheme, explicit Euler method and a fractional variant of the Crank-Nicolson method. The main tools for the analysis include operator-valued Fourier multiplier theorem due to Weis [48] and its discrete analogue due to Blunck [10]. These results generalize the corresponding results for parabolic problems.

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Bangti Jin, Buyang Li, Zhi Zhou. 2016-06-24. Discrete maximal regularity of time-stepping schemes for fractional evolution equations. https://arxiv.org/abs/1606.07587

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