Existence, uniqueness, and a priori estimates for solutions are studied for stochastic parabolic Ito equations. An analog of the second fundamental inequality and the related existence theorem are obtained for backward stochastic parabolic Ito equation. AMS 1991 subject classification: Primary 60J55, 60J60, 60H10. Secondary 34F05, 34G10.

Upcoming responses in the second of two subsequently performed tasks can speed up compatible responses in the temporally preceding first task. Two experiments extend previous demonstration of such backward compatibility to affective features: Responses to affective stimuli were faster in Task 1 when an affectively compatible response effect was anticipated for Task 2. This emotional backward co...

In order to solve backward parabolic problems F. John [Comm. Pure. Appl. Math. (1960)] introduced the two constraints “‖u(T )‖ ≤ M” and ‖u(0) − g‖ ≤ δ where u(t) satisfies the backward heat equation for t ∈ (0, T ) with the initial data u(0). The slow-evolution-from-the-continuation-boundary (SECB) constraint has been introduced by A. Carasso in [SIAM J. Numer. Anal. (1994)] to attain continuou...

The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state...

We rigorously prove that the semidiscrete schemes of a Perona-Malik type equation converge, in a long time scale, to a suitable system of ordinary differential equations defined on piecewise constant functions. The proof is based on a formal asymptotic expansion argument, and on a careful construction of discrete comparison functions. Despite the equation has a region where it is backward parab...

In order to solve backward parabolic problems F. John [Comm. Pure. Appl. Math. (1960)] introduced the two constraints “‖u(T )‖ ≤ M” and ‖u(0) − g‖ ≤ δ where u(t) satisfies the backward heat equation for t ∈ (0, T ) with the initial data u(0). The slow-evolution-from-the-continuation-boundary (SECB) constraint has been introduced by A. Carasso in [SIAM J. Numer. Anal. (1994)] to attain continuou...

We determine new, more favourable, and in a sense optimal, multipliers for the threeand five-step backward difference formula (BDF) methods. We apply the new multipliers to establish stability of these methods as well as of their implicit–explicit counterparts for parabolic equations by energy techniques, under milder conditions than the ones recently imposed in [4, 1].

A new method of optimization on linear parabolic solar collectors using exergy analysis is presented. A comprehensive mathematical modeling of thermal and optical performance is simulated and geometrical and thermodynamic parameters were assumed as optimization variables. By applying a derived expression for exergy efficiency, exergy losses were generated and the optimum design and operating co...

Waldén, Karlson, and Sun found an elegant explicit expression of backward error for the linear least squares problem. However, it is difficult to compute this quantity as it involves the minimal singular value of certain matrix. In this paper we present a simple estimation to this bound which can be easily computed especially for large problems. Numerical results demonstrate the validity of the...

Dedicated to William Kahan and Beresford Parlett on the occasion of their 60th birthdays Let A be an m n matrix, b be an m-vector, and x̃ be a purported solution to the problem of minimizing kb Axk2. We consider the following open problem: find the smallest perturbation E of A such that the vector x̃ exactly minimizes kb (A+E)xk2. This problem is completely solved whenE is measured in the Frobeni...