2010 | OriginalPaper | Chapter
Analysis of the Diffusion Equation
Authors : Aslak Tveito, Hans Petter Langtangen, Bjørn Frederik Nielsen, Xing Cai
Published in: Elements of Scientific Computing
Publisher: Springer Berlin Heidelberg
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In Chap. 7 we studied several aspects of the theory of diffusion processes. We saw how these equations arise in models of several physical phenomena and how they can be approximately solved by suitable numerical methods. The analysis of diffusion equations is a classic subject of applied mathematics and of scientific computing. Its impact on the field of partial differential equations (PDEs) has been very important, both from a theoretical and practical point of view. The purpose of this chapter is to dive somewhat deeper into this field and thereby increase our understanding of this important topic.