Current Research:

My scientific interests lie in the following areas: (a) development of asymptotic reduction procedures for complex high dimensional applied models; (b) perturbation methods and their applications to the problems of mathematical biology, ecology, chemical kinetics, neuroscience modeling and other fields; (c) construction and justification of asymptotic expansions for solutions of singularly perturbed ordinary and partial differential equations and systems. Modeling age structure dynamics of trees in a natural forest in the presence of a disease was a topic of M.A. thesis of a graduate students that I recently advised (the project was completed in 2005).

Recent Publications:

L. V. Kalachev, Asymptotic methods: application to reduction of models, Natural Resource Modeling (2000), V. 13, No. 3, pp. 305 - 338.

H. Haario and L. Kalachev, Asymptotic analysis of a complex reaction scheme in solid-liquid system, Chem. Eng. Sci.(2003), Vol. 58, pp. 2823-2834.

M. Kraemer, L. Kalachev, and D. Coble, A class of models describing age structure dynamics in a natural forest, Natural Resource Modeling (2002), Vol. 15, No. 2, pp. 149-200.

S. Handrock-Meyer, L. Kalachev, and K. Schneider, A method to determine the dimension of long-time dynamics in multi-scale systems, J. Math. Chem. (2001), Vol. 30, No. 2, pp. 133-160.

L. Kalachev, and K. Schneider, Global behavior and asymptotic reduction of a chemical kinetics system with continua of equilibria, J. Math. Chem. (2005), Vol. 37, No. 1, pp. 57-74.