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发帖数: 520 | 1 We consider a parabolic equation: u_t=au_xx+bu_x+cu, x in R, 0
If the coefficients a, b, c have good enough behavior, e.g. analytic, can we
get the following conclusion?
If the solution is not identical constant, then for any 0
R, the set A(t)={x in R: u(x,t)=r} is a discrete subset of R.
Angenent said that if r=0, then this conclusion is trivial. It is Theorem A
of the following paper.
http://www.math.jhu.edu/~js/Math745/angenent.par1.pdf
I do not know how to prove Theorem A of Angenent. And I want to know if my
stronger conclusion is correct. Thank you for any help. |
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