Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications (with J. Mierczynski), to appear in the Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics Series, edited by Brezis, Douglas and Jeffrey, CRC Press

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Abstract: The goal of the monograph is to give a clear and essentially self-contained account of the spectral theory, in particular, the theory of principal spectrum and principal Lyapunov exponents for general time dependent and random linear parabolic equations of second order on bounded domain, as well as systems of such equations. Also, applications to uniform persistence in nonlinear Kolmogorov systems are given.

The monograph gives a unified approach to the theory of principal spectrum: It starts from the abstract general theory, in the framework of weak solutions, and then specializes to the cases of random and nonautonomous equations. Fundamental properties of the principal spectrum/principal Lyapunov exponents are investigated. The book contains many new results, as well as it puts already known results in a new perspective.

The intended readership of the monograph are research mathematicians and Ph. D. students in mathematics, in particular (but not limited to) those specializing in applications of mathematics to ecology.