What exactly does blow up mean, when people say, for example, that a solution (to a pde (say)) blows up.
Thanks.
soft-questionterminologypde
asked 2010-08-19
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Hmm, my understanding of "blow-up" in the context of partial differential equations is that is what happens when, due to singularities inherent in the set of solutions to a PDE, inaccuracies in the approximate solution appear when attempting to approximate the solution with a mesh. Usually this is because the user of the algorithm for solving the PDE may have failed to use the proper dependent variables, neglected to factor out singular behavior, or any number of other things. – 2010-08-19
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Shibi, I think you're asking about blowup in PDEs, which is much more specific and well-defined than "blow up" in the sense several of the answers seem to be taking it. If you could clarify if you mean PDEs, that would be very helpful. – 2010-08-19
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Katie: "that a solution (to a pde (say)) blows up" Granted, he neglected to capitalize... – 2010-08-19
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sure but the "say" makes it seem like a PDE is just an arbitrary example of a possible answer that could be of interest, not the actual question. (I don't care to be nitpicky, except that this formulation of the question is receiving answers that vary widely and in un-useful ways in their interpretation of what the question is; see, e.g. Dan Z's comment on his answer.) – 2010-08-19
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Katie, I did mean it in the sense of PDE's , or in a sense of a function in calculus ( which is the reason I put a say in the brackets). Sorry to have caused the confusion. – 2010-08-22