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May 9, 2017 at 16:02 comment added xzczd @user64494 I've rephrased my answer to make it more prudent.
May 9, 2017 at 11:07 history edited xzczd CC BY-SA 3.0
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May 8, 2017 at 17:31 history edited xzczd CC BY-SA 3.0
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May 8, 2017 at 13:33 history edited xzczd CC BY-SA 3.0
Remove abrupt conclusion to make the answer more "strict"
May 8, 2017 at 11:01 comment added user64494 I prefer solid arguments supplied with codes and references over unbased words. @xzczd
May 8, 2017 at 8:37 comment added xzczd @user64494 Then I think LaplaceTransform, which is essentially a integration, plays exactly the role of that "condition". As to the i.c., the definition in the wiki page doesn't have any requirement for it, and I think the "problem" with i.c. does not contradict the definition: if the weak solution may not satisfy the equation in some "region", then why can't it be on the boundary?
May 8, 2017 at 8:17 comment added user64494 Your statement about a weak solution is unbased. Up to en.wikipedia.org/wiki/Weak_solution , a weak solution must satisfy the condition after " then an integrable function u would be said to be a weak solution if" in the cited Wiki article. This condition is not verified by you. Also there are problems with IC. @xzczd:
May 8, 2017 at 7:52 comment added xzczd To the downvoter, I am interested in what was missing from my answer, would you please elaborate? I'm not trying to complain here, I'm just curious about what I can do to improve my answer.
May 8, 2017 at 6:06 history edited xzczd CC BY-SA 3.0
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May 8, 2017 at 5:12 history edited xzczd CC BY-SA 3.0
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May 8, 2017 at 4:23 history answered xzczd CC BY-SA 3.0