How Are BV Functions Applied in Physics and Engineering?

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Discussion Overview

The discussion centers around the application of functions of bounded variation (BV functions) in physics and engineering. Participants seek specific examples and clarifications regarding the relevance of BV functions in various scientific fields, particularly mechanics and chemical kinetics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the relevance of BV functions in physics and engineering, seeking examples to validate claims made in a mathematical text.
  • Another participant asserts that BV functions are widely used in applied sciences due to their ability to handle discontinuities, citing applications in mechanics, physics, and chemical kinetics.
  • A participant expresses frustration with the lack of specific examples in existing literature, despite acknowledging the general claims about the applications of BV functions.
  • A later reply provides a specific reference to a page in a book discussing eigenvalues and eigenfunctions in quantum physics, suggesting a potential application of BV functions in that context.

Areas of Agreement / Disagreement

Participants do not reach a consensus on specific applications of BV functions, with some expressing the need for more detailed examples while others reference general uses in various fields.

Contextual Notes

Some participants note the limitations of existing resources, indicating a lack of specific physical applications and page references in the literature they have consulted.

Hjensen
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I am reading about a branch of mathematics which does not allow separable spaces. The author of the text gives the space of functions of bounded variation as an example of a non-separable space, which is fine - except for the fact that he goes on to claim that "this space is relevant to both physicists and engineers" without giving any further elaboration.

So my question is this: Do any of you have a few examples of BV-functions being used in physics or engineering? I don't need a detailed explanation, I just need to convince myself that the argument given in my book is actually important.
 
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The ability of BV functions to deal with discontinuities has made their use widespread in the applied sciences: solutions of problems in mechanics, physics, chemical kinetics are very often representable by functions of bounded variation. The book (Hudjaev & Vol'pert 1985) details a very ample set of mathematical physics applications of BV functions. Also there is some modern application which deserves a brief description.

http://en.wikipedia.org/wiki/Bounded_variation"

You might want to check out "Analysis in classes of discontinuous functions and equations of mathematical physics":
http://books.google.com/books?id=lA...tinuous+functions"&hl=en#v=onepage&q&f=false"
 
Last edited by a moderator:
dlgoff said:
http://en.wikipedia.org/wiki/Bounded_variation"

You might want to check out "Analysis in classes of discontinuous functions and equations of mathematical physics":
http://books.google.com/books?id=lA...tinuous+functions"&hl=en#v=onepage&q&f=false"

I did have a look at Wikipedia before writing here. However, all it states is that BV functions have uses in mechanics, physics and chemical kinetics. I would have liked something a bit more specific. As for the book, it goes through the theory of BV - which I am already familiar with - but I can't find any physical applications of it. If you know a page number on which I could find this, I would appreciate it. Thanks for your time.
 
Last edited by a moderator:

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