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L∞(L2) and L∞(L∞) error estimates for mixed methods for integro-differential equations of parabolic type

Ziwen Jiang (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Error estimates in L∞(0,T;L2(Ω)), L∞(0,T;L2(Ω)2), L∞(0,T;L∞(Ω)), L∞(0,T;L∞(Ω)2), Ω in 2 , are derived for a mixed finite element method for the initial-boundary value problem for integro-differential equation u t = div { a u + 0 t b 1 u d τ + 0 t 𝐜 u d τ } + f based on the Raviart-Thomas space Vh x Wh ⊂ H(div;Ω) x L2(Ω). Optimal order estimates are obtained for the approximation of u,ut in L∞(0,T;L2(Ω)) and the associated velocity p in L∞(0,T;L2(Ω)2), divp in L∞(0,T;L2(Ω)). Quasi-optimal order estimates are obtained for the approximation...

Local center manifold for parabolic equations with infinite delay

Hana Petzeltová (1994)

Mathematica Bohemica

The existence and attractivity of a local center manifold for fully nonlinear parabolic equation with infinite delay is proved with help of a solutions semigroup constructed on the space of initial conditions. The result is applied to the stability problem for a parabolic integrodifferential equation.

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