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This article deals with the uniqueness in identifying multiple parameters simultaneously in the one-dimensional time-fractional diffusion-wave equation of fractional time-derivative order $in (0,2)$ with the zero Robin boundary condition. Using the Laplace transform and a transformation formula, we prove the uniqueness in determining an order of the fractional derivative, a spatially varying potential, initial values and Robin coefficients simultaneously by boundary measurement data, provided that all the eigenmodes of an initial value do not vanish. Furthermore, for another formulation of inverse problem with input source term in place of initial value, by the uniqueness in the case of non-zero initial value and a Duhamel principle, we prove the simultaneous uniqueness in determining multiple parameters for a time-fractional diffusion-wave equation.
We prove existence and uniqueness of distributional, bounded, nonnegative solutions to a fractional filtration equation in ${mathbb R}^d$. With regards to uniqueness, it was shown even for more general equations in [19] that if two bounded solutions
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 derivat
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field associate
We study the wave equation on infinite graphs. On one hand, in contrast to the wave equation on manifolds, we construct an example for the non-uniqueness for the Cauchy problem of the wave equation on graphs. On the other hand, we obtain a sharp uniq
In this paper, we discuss the uniqueness for solution to time-fractional diffusion equation $partial_t^alpha (u-u_0) + Au=0$ with the homogeneous Dirichlet boundary condition, where an elliptic operator $-A$ is not necessarily symmetric. We prove tha