Timeline for What is the motivation to define measure valued solutions to a PDE model?
Current License: CC BY-SA 4.0
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| Mar 3, 2020 at 16:56 | history | edited | Willie Wong |
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| Mar 3, 2020 at 16:06 | comment | added | Mark | I don't know this concrete equation but I know many similar. The thing that you should remember (and @IgorKhavkine explained it well) is that if you work on PDE problems of this kind, you can't only have pointwise solutions (that is kinda rare). You'll usually have some weak solutions such as measure-valued solutions, solutions in the distribution sense, etc. | |
| Mar 3, 2020 at 11:36 | comment | added | Manoj Kumar | @IgorKhavkine yes, that is what I was missing, because solution here in my case is a solution of the population model. | |
| Mar 3, 2020 at 10:58 | history | edited | Manoj Kumar | CC BY-SA 4.0 |
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| Mar 3, 2020 at 10:51 | comment | added | Igor Khavkine | Perhaps you are just confused by the terminology? The domain of your solution is a set, $\mathbb{R}^+$ in this case. While pointwise values $\mu(t,x)$ do not make sense for a measure, what does make sense is any integral of the form $\int_a^b w(x)\mu(t,x)$, giving you a weighted average of $w(x)$ over the interval $x\in[a,b]$ with respect to $\mu(t)$, a "population distribution" in your case. Perhaps such weighted averages are all that you need from your solution. | |
| Mar 3, 2020 at 8:20 | history | asked | Manoj Kumar | CC BY-SA 4.0 |