Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
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In this paper, the authors considered the initial value/boundary value problems for fractional diffusion-wave equation and established the unique existence of the weak solution and the asymptotic behavior as the time t goes to ∞ and the proofs are based on the eigenfunction expansions.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2011-10-01 and is currently open access. It has received 965 citations till now. The article focuses on the topics: Boundary value problem & Initial value problem.read more
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Two Fully Discrete Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data
TL;DR: Two fully discrete schemes based on the piecewise linear Galerkin finite element method in space and convolution quadrature in time with the generating function given by the backward Euler method/second-order backward difference method are developed and establish error estimates optimal with respect to the regularity of problem data.
Journal ArticleDOI
The Galerkin finite element method for a multi-term time-fractional diffusion equation
TL;DR: The initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain is considered and nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived.
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An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data
TL;DR: In this article, the error analysis of the L1 scheme was revisited, and an O( √ 2−ε ) convergence rate was established for both smooth and nonsmooth initial data.
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A tutorial on inverse problems for anomalous diffusion processes
Bangti Jin,William Rundell +1 more
TL;DR: In this article, the degree of ill-posedness of fractional diffusion inverse problems was examined using the two-parameter Mittag-Leffler function and singular value decomposition.
References
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A Remark on Simple Scattering Theory
TL;DR: In this paper, a new proof of the existence and asymptotic completeness of wave operators is given with utilizing the smooth operator technique, which is based on the smooth wave operator technique.
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Fractional Differentiation and its Applications (FDA08)
TL;DR: The Fractional Differentiation and its Applications (FDA08) workshop as discussed by the authors was the third in an ongoing series of conferences dedicated to exploring applications of fractional calculus in science, engineering, economics and finance.
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The second main theorem of hypersurfaces in the projective space
TL;DR: In this paper, a meromorphic partial projective connection is defined for a holomorphic map from the complex plane to the n-dimensional complex projective space, which is shown to be geodesic with respect to these hypersurfaces.
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A remark on Malliavin Calculus : Uniform Estimates and Localization
TL;DR: In this article, the authors showed that these estimates can be uni-formized and localized similarly to the heat operators associated with Hormander type degenerate elliptic operators.
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