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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Identifying a Space-Dependent Source Term and the Initial Value in a Time Fractional Diffusion-Wave Equation
Xianli Lv,Xiufang Feng +1 more
TL;DR: In this paper , a mollification regularization method based on a bilateral exponential kernel is presented to solve the ill-posedness of the problem for the first time, and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter.
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Existence of Solution of Space–Time Fractional Diffusion-Wave Equation in Weighted Sobolev Space
TL;DR: In this article, the authors considered the Cauchy problem of space-time fractional diffusion-wave equation and established the existence of solution in terms of Mittag-Leffler function and proved its uniqueness in weighted Sobolev space by use of Mikhlin multiplier theorem.
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The virtual element method for the time fractional convection diffusion reaction equation with non-smooth data
Yadong Zhang,Minfu Feng +1 more
TL;DR: In this article , an efficient virtual element method was developed to solve the two-dimensional time fractional convection diffusion reaction equation involving the Caputo fractional derivative with non-smooth solutions in the time direction.
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Existence and uniqueness of a weak solution to fractional single-phase-lag heat equation
TL;DR: In this paper , the existence and uniqueness of a weak solution to the fractional single-phase lag heat equation was studied and a variational approach was employed to show the uniqueness of this weak solution.
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Bernstein modal basis: application to the spectral Petrov-Galerkin method for fractional partial differential equations
TL;DR: In this article, a spectral Petrov-Galerkinetic method for non-orthogonal dual Bernstein polynomials is presented, which leads to banded sparse linear systems for problems with constant coefficient.
References
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TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
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Elliptic Partial Differential Equations of Second Order
David Gilbarg,Neil S. Trudinger +1 more
TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
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TL;DR: In this article, the authors considered the generation and representation of a generator of C0-Semigroups of Bounded Linear Operators and derived the following properties: 1.1 Generation and Representation.
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Theory and Applications of Fractional Differential Equations
TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.