Mathematics Colloquium: Optimization Models with Delays in Economics, the Environment, and Population Biology

2009-05-13

4:10 p.m. Neill Hall 416

Natali Hritonenko

Abstract: The talk is an overview of the speaker’s recent results in the areas of optimization and modeling of dynamic processes in economics, the environment, and population biology. The following topics are considered: (1)Integral equations with distributed and endogenous delays and equations with delays and leads: theoretical issues and applied importance. (2)Vintage capital models: the optimal dynamics of equipment lifetime under technological change and technological breakthroughs, structural properties and turnpike theorems, replacement and anticipation echoes, zero-investment period. (3)PDE-based vintage capital models with distributed investment. (4)Age-dependent nonlinear integral models of a single species population with intra-species competition: bifurcation analysis, optimal exploitation, maximization of harvesting return, bang-bang controls. (5)Size-structured nonlinear PDE-integral models of forest management with carbon sequestration. (6)Optimal adaptation and abatement investments in long-term climate policies in a one-sector growth model with Cobb-Douglas technology and the environmental quality. (The speaker is a candidate for Applied Math or Statistics on WSU-Vancouver Campus)