The scalar reaction-diffusion equation $$ u_t=u_{xx}+f(u)~~(*) $$ with some non-linearity $f(u)$ is a semi-linear parabolic pde.

I know that for linear parabolic pde there are the weak maximum principle and the strong maximum principle, see here https://en.wikipedia.org/wiki/Maximum_principle.

I guess these does, in general, not hold semi-linear parabolic pde as $(*)$?

Are there similar statements?


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