in this paper, the optimal boundary control problem for distributed parabolic systems, involving second orderoperator with an infinite number of variables, in which constant lags appear in the integral form both in the state equations and in the boundary condition is considered. some specific properties of the optimal control arediscussed.

The Dirichlet problem for non-divergence parabolic equations with discontinuous in time coefficients.

sorption reactions in many heterogeneous systems are important. adsorption is a time dependent process and knowing the adsorption rate is essential for designing, evaluating and recovering the adsorbents. at the present study, an ammonium adsorption kinetic experiment by some soils series of golestan provice, which is varying in mineralogical and textural properties was conducted using solution...

Transient excitation currents generate electromagnetic fields which, in turn, induce electric currents in proximal conductors. For slowly varying fields, this can be described by the eddy current equations, which are obtained by neglecting the dielectric displacement currents in Maxwell’s equations. The eddy current equations are of parabolic-elliptic type: In insulating regions, the field inst...

We prove the interior null–controllability of one–dimensional parabolic equations with time independent measurable coefficients.

There are many nonlinear parabolic equations whose solutions develop singularity in finite time, say T. In many cases, a certain norm of the solution tends to infinity as time t approaches T. Such a phenomenon is called blow-up, and T is called the blow-up time. This paper is concerned with approximation of blow-up phenomena in nonlinear parabolic equations. For numerical computations or for ot...

We consider parabolic equations in nondivergent form with discontinuous coefficients at higher derivatives. Their investigation is most complicated because, in general, in the case of discontinuous coefficients, the uniqueness of a solution for nonlinear parabolic or elliptic equations can fail, and there is no a priory estimate for partial derivatives of a solution. There are some conditions t...

In this paper, for the numerical approximation of random partial differential equations (RPDEs) of parabolic type, an explicit higher order finite difference scheme is constructed. In continuation the main properties of deterministic difference schemes, i.e. consistency, stability and convergency are developed for the random cases. It is shown that the proposed random difference scheme has thes...