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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The Calderón problem for the fractional Schrödinger equation
TL;DR: In this paper, the authors show global uniqueness in an inverse problem for the fractional Schrodinger equation, where an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions.
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Two regularization methods to identify a space-dependent source for the time-fractional diffusion equation
TL;DR: In this article, the inverse problem of identifying a space-dependent source for the time-fractional diffusion equation is investigated, where the time derivative is replaced with a Caputo derivative of order.
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Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction-diffusion equation
TL;DR: In this paper, the authors considered a reaction diffusion problem with an unknown nonlinear source function that has to be determined from overposed data and derived a uniqueness result and a numerical algorithm with some theoretical qualification.
Overview to mathematical analysis for fractional diffusion equations - new mathematical aspects motivated by industrial collaboration
TL;DR: In this paper, the authors discuss a fractional diffusion equation which has been studied already comprehensively from the theoretical interests, but the researches are expanded as a mathematical topic in view of the industrial applications.
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An Lq(Lp)-theory for the time fractional evolution equations with variable coefficients
TL;DR: In this paper, an L q (L p ) -theory for the semilinear fractional equations of the type (0.1) ∂ t α u ( t, x ) was introduced.
References
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Book
Partial Differential Equations
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.
Book
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.
Book
Semigroups of Linear Operators and Applications to Partial Differential Equations
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.
Book
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.