Mathematical Sciences: Reaction-Diffusion Equations: Asymptotic Problems, Random Perturbations, Probabilistic Approach

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The principal investigator is a leading researcher in the area of perturbation theory and reaction diffusion equations. He has done fundamental work on small random perturbations of dynamical systems and many of his results continue to be a corner stone in the current research in the field. The project proposes 20 hard and unsolved problems. The subject matter involves both stochastic processes and partial differential equations. The major areas of application arise in engineering and biology. In particular, the investigator will explore the relationships of partial differential equations with Markov processes. Random perturbations of infinite dimensional dynamical systems and semiflows will be studied.