https://dispersivewiki.org/DispersiveWiki/index.php?title=Fundamental_solution&feed=atom&action=historyFundamental solution - Revision history2024-03-29T05:01:44ZRevision history for this page on the wikiMediaWiki 1.39.3https://dispersivewiki.org/DispersiveWiki/index.php?title=Fundamental_solution&diff=3939&oldid=prevTao at 04:32, 10 August 20062006-08-10T04:32:27Z<p></p>
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In a [[well-posed]] [[linear]] equation, the solution is given in terms of the initial data via a linear operator. The kernel of that operator (which may be only a distribution) is then the '''fundamental solution''' of the equation. Another way of viewing this is that the fundamental solution is the solution associated to initial data which is a Dirac delta function. Since every function is (formally, at least) a superposition of delta functions, by the [[principle of superposition]] every solution is thus a superposition of fundamental solutions.<br />
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