This paper is concerned with Sobolev weak solution of Hamilton-Jacobi-Bellman (HJB) equation. This equation is derived from the dynamic programming principle in the study of the stochastic optimal control problem. Adopting Doob-Meyer decomposition theorem as one of main tool, we prove that the optimal value function is the unique Sobolev weak solution of the corresponding HJB equation. For the ...

g(0) > 0 and lim u→∞ g(u) u = ∞. We consider solutions u of (1.1) which are nonnegative in Ω. Typical examples are g(u) = e and g(u) = (1+u) with p > 1. Problem (1.1) and its connections with combustion theory have been extensively studied; see [CR], [G], [JL], [BCMR] and [BE]. It is known that there exists 0 < λ∗ < ∞ such that (i) for 0 ≤ λ < λ∗, there is a minimal classical solution uλ of (1....

As a new approach, the acidity that wood exhibits under moderate conditions is assayed by stimulated dissociation of weak wood acids in lightly basic secondary phosphate solutions. To assure a sufficient dissociation of hardly soluble weak acids in the solution, the amount of wood suspended in Na(2)HPO(4) solutions should be small but vary depending on the degree of acidity of wood species. How...

This paper is concerned with Sobolev weak solution of Hamilton-Jacobi-Bellman (HJB) equation. This equation is derived from the dynamic programming principle in the study of the stochastic optimal control problem. Adopting Doob-Meyer decomposition theorem as one of main tool, we prove that the optimal value function is the unique Sobolev weak solution of the corresponding HJB equation. For the ...

the silver spr chip was modified by alkaline-silane condensation with aminopropyltriethoxysilane (aptes) in naoh aqueous solution at different times. silver sputtered slides coated with aptes were immersed in naoh solution, enabling us to produce silver surfaces homogeneously covered with aptes. the surface properties of grafted aptes on sputtered silver surface as a occasion of time were studi...

In this paper we propose a new notion of Forward-Backward Martingale Problem (FBMP), and study its relationship with the weak solution to the backward stochastic differential equations. The FBMP extends the idea of the well-known (forward) martingale problem of Stroock and Varadhan, but it is structured specifically to fit the nature of a forward-backward stochastic differential equation (FBSDE...