Abstract
This chapter discusses the blow-up in nonlinear heat equations from the dynamical systems point of view. Over the past decade, the dynamical systems theory has proved extremely useful in the study of blow-up problems. In some cases, it provided powerful analytical tools to reveal the fine structure of singularities or to understand some global features of blow-up solutions. In other cases, where the dynamical systems theory does not apply rigorously because of lack of some crucial estimates, its ideas nonetheless served as a reliable guiding principle in making right conjectures. The chapter describes center manifold theory and discusses whether solutions have a continuation beyond the blow-up time.
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