It is shown that a function u satisfying |∂t + u| M (|u| + |∇u|), |u(x, t)| MeM|x| in (R \ BR) × [0, T ] and u(x, 0) = 0 for x ∈ R \ BR must vanish identically in R \ BR × [0, T ].

The analyses of interior penalty discontinuous Galerkin methods any order k for solving elliptic and parabolic problems with Dirac line sources are presented. For the steady state case, we prove convergence method by deriving a priori error estimates in L 2 norm weighted energy norms. In addition, almost optimal local approximation order. Further, obtained case piecewise linear approximations w...

In this paper a new method based on fuzzy theory is developed to solve the project scheduling problem under fuzzy environment. Assuming that the duration of activities are trapezoidal fuzzy numbers (TFN), in this method we compute several project characteristics such as earliest times, latest times, and, slack times in term of TFN. In this method, we introduce a new approach which we call modif...

We consider a controlled state equation of parabolic type on the halfline (0,+∞) with boundary conditions of Dirichlet type in which the unknown is equal to the sum of the control and of a white noise in time. We study finite horizon and infinite horizon optimal control problem related by menas of backward stochastic differential equations.

The work concerns a type of backward multivalued McKean-Vlasov stochastic differential equations. First, we prove the existence and uniqueness solutions for equation. Then, it is presented that first components their depend continuously on terminal values. Finally, give probabilistic interpretation viscosity nonlocal quasi-linear parabolic variational inequalities.

A quadratic optimal control problem governed by parabolic equations with integral constraints is considered. A fully discrete finite element scheme is constructed for the optimal control problem, with finite elements for the spatial but the backward Euler method for the time discretisation. Some superconvergence results of the control, the state and the adjoint state are proved. Some numerical ...