Uniqueness for inverse problems of determining orders of multi-term time-fractional derivatives of diffusion equation
نویسندگان
چکیده
منابع مشابه
Existence and uniqueness in an inverse source problem for a one-dimensional time-fractional diffusion equation
In this study, an inverse source problem for a one-dimensional timefractional diffusion equation is considered. An existence theorem based on the minimization of an error functional between the output data and the additional data is proved. Then it is showed that the unknown source function can be determined uniquely by an additional data u(0, t), 0 ≤ t ≤ T using an auxiliary uniqueness result ...
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Article history: Received 5 February 2010 Available online 26 August 2010 Submitted by P. Broadbridge
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We consider a one-dimensional fractional diffusion equation: ∂α t u(x, t) = ∂ ∂x ( p(x) ∂u ∂x (x, t) ) , 0 < x < `, where 0 < α < 1 and ∂α t denotes the Caputo derivative in time of order α. We attach the homogeneous Neumann boundary condition at x = 0, ` and the initial value given by the Dirac delta function. We prove that α and p(x), 0 < x < `, are uniquely determined by data u(0, t), 0 < t ...
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ژورنال
عنوان ژورنال: Applicable Analysis
سال: 2014
ISSN: 0003-6811,1563-504X
DOI: 10.1080/00036811.2014.926335