Could someone help me with the following problem: Find all smooth functions u: R x [0, +infinity) ->R with the property that both u and u^n are solutions of the heat equation for some integer n>=2.
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Originally Posted by ruggles Could someone help me with the following problem: Find all smooth functions u: R x [0, +infinity) ->R with the property that both u and u^n are solutions of the heat equation for some integer n>=2. I do not know if this will help, but It may give you somewhere to start. let be solutions to the heat equation let plugging the above into the heat eqaution gives Now if we get Maybe you can figure something out from here. I hope this helps. Good luck.
Last edited by TheEmptySet; May 20th 2008 at 12:57 PM.
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