超临界流体
数学
应用数学
材料科学
物理
热力学
出处
期刊:Elsevier eBooks
[Elsevier]
日期:2005-01-01
卷期号:: 105-158
被引量:12
标识
DOI:10.1016/s1874-5717(06)80005-8
摘要
For some nonlinear parabolic equations, solutions may not exist globally for t ≥ 0, but may become unbounded in finite time. This phenomenon is called “blow-up” and it has been intensively studied in connection with various fields of science, such as plasma physics, the combustion theory, and population dynamics. The chapter discusses blow-up of the solutions of supercritical parabolic equations. It also discusses the connection of equilibria by blow-up solutions. In the qualitative theory of one-dimensional parabolic equations, much effort has been devoted to the study of the connection problem—determining that equilibria are connected by heteroclinic orbits. Under several circumstances, a solution that blows up at a finite time T cannot be continued as an L 1- solution beyond T . This phenomenon is called “complete blow-up.”
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