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Nonlinear Wave Equations, Formation of Singularities (University Lecture Series)

liliangmatn 添加于 2014-6-2 19:38 | 1519 次阅读 | 0 个评论

作者
Fritz John
摘要
This is the second volume in the University Lecture Series, designed to make more widely available some of the outstanding lectures presented in various institutions around the country. Each year at Lehigh University, a distinguished mathematical scientist presents the Pitcher Lectures in the Mathematical Sciences. This volume contains the Pitcher lectures presented by Fritz John in April 1989. The lectures deal with existence in the large of solutions of initial value problems for nonlinear hyperbolic partial differential equations. As is typical with nonlinear problems, there are many results and few general conclusions in this extensive subject, so the author restricts himself to a small portion of the field, in which it is possible to discern some general patterns. Presenting an exposition of recent research in this area, the author examines the way in which solutions can, even with small and very smooth initial data, ``blow up\'\' after a finite time. For various types of quasi-linear equations, this time depends strongly on the number of dimensions and the ``size\'\' of the data. Of particular interest is the formation of singularities for nonlinear wave equations in three space dimensions.
详细资料
- 文献种类: Book Whole
- 期卷页: 64页
- 出版社: American Mathematical Society
- ISBN: 9780821870013
学科领域自然科学 » 数学
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Nonlinear Wave Equations, Formation of Singularities (University Lecture Series)
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