»ã±¨±êÌâ (Title)£ºError analysis of spectral method for fractional optimal control problems (·ÖÊý½××îÓŽÚÔìÎÊÌâµÄÆײ½ÖèµÄÎó²î·ÖÎö)

»ã±¨ÈË (Speaker)£º³ÂÑÞƼ ½ÌÊÚ£¨ÄϾ©Óʵç´óѧ£©

»ã±¨¹¦·ò (Time)£º2024Äê6ÔÂ4ÈÕ(Öܶþ) 10:00-12:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿F309

Ô¼ÇëÈË(Inviter)£ºÀƷ¡¢²ÌÃô

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»ã±¨ÌáÒª£ºIn this talk, we investigate an optimal control problem governed by a time fractional diffusion equation with non-homogeneous boundary condition. We construct a suitable weak formulation, study its well-posedness, and develop a spectral Galerkin method for its numerical solution. The main contributions of this work are: 1) the study of optimality conditions, which is crucial for analyzing the optimal control problem; 2) the derivation of a priori error estimates for the space-time spectral approximation; 3) the derivation of a posteriori error estimates for the state, costate, and control approximations; 4) the conduct of numerical experiments to confirm the efficiency of the proposed method. The obtained numerical results demonstrate exponential convergence for smooth exact solutions.