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##### Chapter 3 / Re: Chapter 3.2 Problem 9

« Last post by**Zicheng Ding**on

*February 06, 2022, 02:19:29 PM*»

I am thinking that if we assume maximum is not on the boundary, then in the initially with $u_t = ku_{xx}$ we will have $u_t - ku_{xx} < 0$ as a contradiction, but in this case we will not necessarily have $u_t - xu_{xx} < 0$ since $x$ can switch signs, so we no longer have the contradiction and that breaks down the proof.