A Stability Technique for Evolution Partial Differential Equations

The book A Stability Technique for Evolution Partial Differential Equations. A Dynamical Systems Approach by Victor A. Galaktionov and Juan Luis Vazques, outstanding mathematicians in the field of partial differential equations, introduces a new approach to asymptotic large-time analysis of evolution partial differential equations. This approach is based on authors’ stability result formulated in the abstract setting of infinite-dimensional dynamical systems in an arbitrary metric space. The new stability theorem states that under certain hypotheses the omegalimit set of a perturbed dynamical system is stable under arbitrary asymptotically small perturbations. In contrast to standard methods, the important feature of this theorem is that it imposes the assumptions not on the original equation but on the limit one. After the precise statement and the proof of the abstract stability theorem in the first chapter, further parts of the book deal with various evolution problems described by nonlinear partial differential equations. The problems analysed include: