مشخصات پژوهش

عنوان	Fr\'{e}chet differentiability and the gradient of the cost functional of an inverse source problem
نوع پژوهش	مقاله ارائه شده کنفرانسی
کلیدواژه‌ها	Inverse source problem‎, ‎time fractional diffusion equation; adjoint problem; Fr\'{e}chet derivative.
چکیده	‎The problem of determining the source term $ f=f(x) $ in a time fractional diffusion equation from the measured data at the final time is formulated‎. ‎To this end‎, ‎a methodology involving minimization of the cost functional is applied and proved that the Fr\'{e}chet derivative of the cost functional can be formulated via the solution of an adjoint problem‎. ‎The obtained results permit one to prove existence and uniqueness of a quasi solution of the considered inverse problems‎, ‎as well as to construct a monotone iteration scheme based on a gradient-type method‎.
پژوهشگران	محمد شهریاری (نفر سوم)، امیر حسین صالحی شایگان (نفر دوم)، علی صفایی (نفر اول)