Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
Reads0
Chats0
TLDR
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
Citations
More filters
Posted Content
Simultaneous uniqueness for multiple parameters identification in a fractional diffusion-wave equation
Xiaohua Jing,Masahiro Yamamoto +1 more
TL;DR: In this paper, the uniqueness in identifying multiple parameters simultaneously in the one-dimensional time-fractional diffusion-wave equation of fractional time-derivative order with the zero Robin boundary condition was established.
Posted Content
Inverse source problems for degenerate time-fractional PDE
Nasser Al-Salti,Erkinjon Karimov +1 more
TL;DR: In this article, the inverse source problems for degenerate time-fractional partial differential equations in rectangular domains were investigated, and the convergence and uniqueness of solutions were discussed, and a new estimate for the generalized Mittag-Leffler type function was established.
Posted Content
On the equivalence of viscosity solutions and distributional solutions for the time-fractional diffusion equation
TL;DR: In this paper, the equivalence of two notions of weak solutions, viscosity solutions and distributional solutions, was proved for an initial-boundary value problem for the time-fractional diffusion equation.
Book ChapterDOI
Inverse Moving Source Problem for Fractional Diffusion(-Wave) Equations: Determination of Orbits
TL;DR: In this paper, the authors derived a Lipschitz stability estimate for the case of a localized moving source by the observation data at d interior points and verified the uniqueness for the general non-localized moving source with additional data of more interior observations.
References
More filters
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.