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Some counterexamples concerning a model of eradication of invasive species
In this note we study the regularity properties of the \emph{Effort Function $E(β)$}. This can be defined as the minimal $L^1$-norm of the control $\tilde α(x) \geq 0$ so that the PDE $$U_t = ΔU + f(U) - \tilde α(t,x) U, \quad U \in [0,1], %\ \tilde α\geq 0,$$ admits a traveling profile $U(x - βt)$
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