Fractional flows driven by subdifferentials in Hilbert spaces

Akagi Goro

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Fractional flows driven by subdifferentials in Hilbert spaces

机译：在希尔伯特空间中由子层次驱动的分数流量

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This paper presents an abstract theory on well-posedness for time-fractional evolution equations governed by subdifferential operators in Hilbert spaces. The proof relies on a regularization argument based on maximal monotonicity of time-fractional differential operators as well as energy estimates based on a nonlocal chain-rule formula for subdifferentials. Moreover, it will be extended to a Lipschitz perturbation problem. These abstract results will be also applied to time-fractional nonlinear PDEs such as time-fractional porous medium, fast diffusion, p-Laplace parabolic, Allen-Cahn equations.

机译：本文介绍了希尔伯特空间中子层次运营商管理的时间分数演化方程的良好姿势的抽象理论。证明依赖于基于时间分数差分运算符的最大单调性的正则化论证以及基于子分类的非识别链规则公式的能量估计。而且，它将扩展到嘴唇扰动问题。这些抽象结果也将应用于时间分数非线性PDE，例如时间分数多孔介质，快速扩散，P-LAPLACE抛物线，艾伦-CAHN方程。

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来源
《Israel Journal of Mathematics》 |2019年第2期|共54页
作者
Akagi Goro;
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作者单位

Tohoku Univ Math Inst Aoba Ku Sendai Miyagi 9808578 Japan;

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正文语种 eng
中图分类数学;
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1. Fractional flows driven by subdifferentials in Hilbert spaces [J] . Akagi Goro Israel Journal of Mathematics . 2019,第Pta2期

机译：在希尔伯特空间中由子层次驱动的分数流量
2. Functional differential equations in Hilbert spaces driven by a fractional Brownian motion [J] . Brahim Boufoussi, Salah Hajji, El Hassan Lakhel Afrika matematika . 2012,第2期

机译：分数布朗运动在希尔伯特空间中的泛函微分方程
3. The Existence and Stability of Inclusion Equations Type of Stochastic Dynamical System Driven by Mixed Fractional Brownian Motion in a Real Separable Hilbert Space [J] . Salah H Abid, Sameer Q Hasan, Zainab A Khudhur Applied Mathematics and Physics . 2017,第1期

机译：实可分Hilbert空间中混合分数布朗运动驱动的随机动力系统包含方程组的存在性和稳定性。
4. Controllability of Nonlinear Stochastic Fractional Integrodifferential Systems in Hilbert Spaces [C] . Rajendran Mabel Lizzy Conference on non-integer order calculus and its applications . 2016

机译：Hilbert空间中非线性随机分数阶积分微分系统的可控性
5. Semilinear stochastic differential equations in Hilbert spaces driven by non-Gaussian noise and their asymptotic properties. [D] . Wang, Li. 2005

机译：非高斯噪声驱动的希尔伯特空间中的半线性随机微分方程及其渐近性质。
6. Vector Generation of Quantum Contextual Sets in Even Dimensional Hilbert Spaces [O] . Mladen Pavičić, Norman D. Megill 2018

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7. Time-dependent Neutral stochastic functional differential equation driven by a fractional Brownian motion in a Hilbert space [O] . Boufoussi, B., Hajji, S., Lakhel, E. 2014

机译：时变中立型随机泛函微分方程由希尔伯特空间中的分数布朗运动驱动
8. Signal Detection in Fractional Gaussian Noise and an RKHS (Reproducing Kernel Hilbert Space) Approach to Robust Detection and Estimation [R] . Barton, R. J. 1989

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Fractional flows driven by subdifferentials in Hilbert spaces

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