Variational solution of fractional advection dispersion equations on bounded domains in ℝd

By Vincent J. Ervin, John Paul Roop. 2007

275 citations recorded by the source corpus.

Subfields: Mechanics of Materials, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ea0fb17acf891a98aafe806d83577aa88153403d

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In Mechanics of Materials

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints (2012, methodology): “As further examples, we note that the use of volume constraints for equations involving the operator L immediately removes the limitation encountered in [7, 30] to only consider a fractional dispersion equation and kernels γ, respectively, where the solutions are in H 0(Ω) for s ∈ (1/2, 1), and to p”
Finite difference methods for two-dimensional fractional dispersion equation (2006, background): “on a finite rectangular domain xL 0 and e(x, y) > 0, and assume that this fractional diffusion equation has a unique and sufficiently smooth solution under the following initial and boundary conditions (some results on existence and uniqueness are developed in [ 14 ]).”
A Crank-Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation (2014, unknown): “We first introduce the spaces J L(Ω), J μ R(Ω), and J μ S (Ω) in R 2 (see [7]).”
Matrix approach to discrete fractional calculus II: Partial fractional differential equations (2008, background): “Ervin and Roop [15, 16 ] presented a theoretical framework for the Galerkin nite element approximation to the steady state fractional advection-diusio n equation, and extended this approach to multidimensional partial dierential equations with constant coecients on the fractional derivative terms.”
A Space-Time Spectral Method for the Time Fractional Diffusion Equation (2009, background): “Note that similar relationships between fractional derivatives and fractional Sobolev spaces have been derived in [6], where the authors first defined the fractional Sobolev spaces on the whole line and then confined them on bounded intervals.”