solutions to the stationary Boltzmann equation in a slab
and error estimates for mixed methods for integro-differential equations of parabolic type
Large time behavior of the solution to an initial-boundary value problem with mixed boundary conditions for a nonlinear integro-differential equation
Large time behavior of the solution to the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. Furthermore, the rate of convergence is given. Initial-boundary value problem with mixed boundary conditions is considered.
Limites hydrodynamiques de l'équation de Boltzmann
L∞(L2) and L∞(L∞) error estimates for mixed methods for integro-differential equations of parabolic type
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 , are derived for a mixed finite element method for the initial-boundary value problem for integro-differential equation 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
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.
Local solution of Carrier's equation in a noncylindrical domain.