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The Galerkin finite element method for a multi-term time-fractional diffusion equation
TLDR
We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Expand
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Strong maximum principle for multi-term time-fractional diffusion equations and its application to an inverse source problem
  • Y. Liu
  • Computer Science, Mathematics
  • Comput. Math. Appl.
  • 23 October 2015
TLDR
We improve the weak maximum principle for the multi-term time-fractional diffusion equation to a stronger one, which is parallel to that for its single-term counterpart. Expand
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Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients
TLDR
In this paper, we investigate the well-posedness and the long-time asymptotic behavior for initial-boundary value problems for multi-term time-fractional diffusion equations. Expand
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Strong maximum principle for fractional diffusion equations and an application to an inverse source problem
Abstract The strong maximum principle is a remarkable property of parabolic equations, which is expected to be partly inherited by fractional diffusion equations. Based on the corresponding weakExpand
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Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations
In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuationExpand
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Inverse source problem for the hyperbolic equation with a time-dependent principal part
Abstract In this paper, we investigate the inverse problem on determining the spatial component of the source term in the hyperbolic equation with a time-dependent principal part. Based on a CarlemanExpand
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Inverse Moving Source Problem for Fractional Diffusion(-Wave) Equations: Determination of Orbits
This paper is concerned with the inverse problem on determining the orbit of a moving source in fractional diffusion(-wave) equations either in a connected bounded domain of \({\mathbb R}^d\) or inExpand
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Theoretical stability in coefficient inverse problems for general hyperbolic equations with numerical reconstruction
In this article, we investigate the determination of the spatial component in the time-dependent second order coefficient of a hyperbolic equation from both theoretical and numerical aspects. By theExpand
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Reconstruction of the Temporal Component in the Source Term of a (Time-Fractional) Diffusion Equation
In this article, we consider the reconstruction of $\rho(t)$ in the (time-fractional) diffusion equation $(\partial_t^\alpha-\triangle)u(x,t)=\rho(t)g(x)$ ($0<\alpha \le 1$) by the observation at aExpand
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Inverse Problems of Determining Sources of the Fractional Partial Differential Equations
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives,Expand
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