Back to Search
Start Over
Global uniqueness in an inverse problem for time fractional diffusion equations
- Publication Year :
- 2016
-
Abstract
- Given $(M,g)$, a compact connected Riemannian manifold of dimension $d \geq 2$, with boundary $\partial M$, we consider an initial boundary value problem for a fractional diffusion equation on $(0,T) \times M$, $T>0$, with time-fractional Caputo derivative of order $\alpha \in (0,1) \cup (1,2)$. We prove uniqueness in the inverse problem of determining the smooth manifold $(M,g)$ (up to an isometry), and various time-independent smooth coefficients appearing in this equation, from measurements of the solution on a subset of $\partial M$ at fixed time. In the "flat" case where $M$ is a compact subset of $\mathbb R^d$, two out the three coefficients $\rho$ (weight), $a$ (conductivity) and $q$ (potential) appearing in the equation $\rho \partial_t^\alpha u-\textrm{div}(a \nabla u)+ q u=0$ on $(0,T)\times \Omega$ are recovered simultaneously.
- Subjects :
- Mathematics - Analysis of PDEs
35R30, 35R11, 58J99
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1601.00810
- Document Type :
- Working Paper