Existence and Uniqueness of the Weak Solution of the Space-Time Fractional Diffusion Equation and a Spectral Method Approximation

By X. Li, Chuanju Xu, 许传炬. 2010

331 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/9a53266cc063e79f852651b887e1011360eb09e6

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Fourier spectral methods for fractional-in-space reaction-diffusion equations (2014, background): “Li and Xu [22] have considered a spectral approach for the weak solution of the space-time fractional diffusion equation.”
A finite element method for time fractional partial differential equations (2011, methodology): “The proof of Theorem 2.1 can be found in [ 19 ].”
A fractional phase-field model for two-phase flows with tunable sharpness: Algorithms and simulations (2016, methodology): “14) (According to a result given in [61] the right-hand-side of (A.”
Numerical solution of time fractional diffusion systems (2017, background): “On the other hand,it is well known that spectral methods can avoid the discretization of the ’heavy tail’ and are exponentially convergent [23, 26, 41, 45, 46] and so are suitable for non-local problems avoiding the difficulty of using time discretization techniques that need to use all, or most, of”
A fractional‐order Jacobi Tau method for a class of time‐fractional PDEs with variable coefficients (2016, unknown): “Li and Xu [28, 29] developed a time–space spectral method for time-fractional diffusion.”
A unified Petrov-Galerkin spectral method for fractional PDEs (2015, methodology): “Li and Xu [29,30] developed a space–time spectral method for a time-fractional diffusion equation with spectral convergence, which was based on the early work of Fix and Roop [31].”
Too much regularity may force too much uniqueness (2016, background): “Time-dependent problems with a fractional temporal derivative of order α ∈ (0, 1) ∪ (1, 2) have attracted much attention in recent years, since these problems arise in several models of physical processes—see the references in [5, 8, 11, 12, 14].”
Efficient and accurate spectral method using generalized Jacobi functions for solving Riesz fractional differential equations (2016, methodology): “Indeed, spectral methods for some FDEs have been proposed in [11,12] where the well-posedness of some FDEs and their spectral approximations have been established; a Crank–Nicolson ADI Spectral method is presented in [26], a class of efficient spectral methods for solving multi-dimensional FDEs have”