Infinite Horizon Boundary Value Problems and Applications

Infinite Horizon Problems

A typical discrete-time sequential decision problem involves a system whose state is assumed to evolve either deterministically or probabilistically over time-periods that are often called stages. This evolution is affected by the decisions a planner makes at the beginning of each stage after observing the system state. The decision maker’s goal then is to optimize some measure of system perfor...

Infinite Horizon Discounted Cost Problems

• We often approximate a large number of periods, even if the horizon is known and finite, by assuming an infinite number of periods, and hope that this assumption will simplify the solution. Indeed, even if the general theory becomes more involved, the solution obtained often is simpler and has important computational and conceptual advantages: in particular, the optimal policy is often statio...

1 Inverse Boundary Value Problems in Applications

Highlights of Results. Here are some of the main results of my research in recent years: (i) Together with my collaborators, we have performed constructive mathematical analysis on elliptic inverse problems in quantitative photoacoustic tomography (QPAT)[8]. The analysis led to not only uniqueness and stability results on the inverse problems but also a direct reconstruction method that is non-...

Boundary Value Problems for Functional Difference Equations on Infinite Intervals

L2-transforms for boundary value problems

In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.