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In this paper, we investigate the well-posedness and the long-time asymptoticbehavior for the initial-boundary value problem for multi-term time-fractionaldiffusion equations, where the time differentiation consists of a finitesummation of Caputo derivatives with decreasing orders in (0,1) and positiveconstant coefficients. By exploiting several important properties ofmultinomial Mittag-Leffler functions, various estimates follow from theexplicit solutions in form of these special functions. Then the uniqueness andcontinuous dependency upon initial value and source term are established, fromwhich the continuous dependence of solution of Lipschitz type with respect tovarious coefficients is also verified. Finally, by a Laplace transformargument, it turns out that the decay rate of the solution as time tends toinfinity is dominated by the minimum order of the time-fractional derivatives.

Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients